TOHOKU UNIVERSITY Researchers - Cavallina Lorenzo

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Cavallina Lorenzo

Section

Graduate School of Science

Job title

Assistant Professor

Degree

Ph.D. (Tohoku University)

researchmap

https://researchmap.jp/cava

J-GLOBAL ID

202001000052297580

e-Rad No.

40881264

ORCID

https://orcid.org/0000-0003-4157-3078

Research History 3

2020/04 - Present

Tohoku University　Graduate School of Science Mathematics, Analysis　Assistant Professor
2018/10 - 2020/03

Japan Society for the Promotion of Science　JSPS Research Fellow: PD
2018/04 - 2018/09

Japan Society for the Promotion of Science　JSPS Research Fellow: DC2

Education 3

Tohoku University　Graduate School of Information Sciences

2015/10 - 2018/09
Università degli Studi di Firenze　Mathematics

2012/10 - 2014/10
Università degli Studi di Firenze　Mathematics

2009/10 - 2012/10

Professional Memberships 2

The Japan Society for Computational Engineering and Science
The Mathematical Society of Japan

Research Interests 9

shape functional
優決定問題
symmetry-asymmetry
composite media
overdetermined problems
shape optimization problems
elliptic and parabolic equations
geometric properties of solutions
Analysis of PDE's

Research Areas 1

Natural sciences / Mathematical analysis / Analysis of PDE's

Awards 2

MSJ Takebe Katahiro Prize

2025/09　The Mathematical Society of Japan　Analysis of overdetermined problems in composite medium
Prominent Research Fellow

2023/07　Tohoku University

Papers 26

Pythagorean Theorem, Law of Sines and Law of Cosines: Alternative Proofs via shape Derivatives Peer-reviewed

Lorenzo Cavallina

Mathematics Magazine　1-6　2025/08/04
Publisher: Informa UK Limited
DOI： 10.1080/0025570x.2025.2535929 　

ISSN： 0025-570X

eISSN： 1930-0980
Visualizing Shape Functionals via Sinkhorn Multidimensional Scaling Peer-reviewed

Toshiaki Yachimura, Jun Okamoto, Lorenzo Cavallina

SIAM Journal on Imaging Sciences　18　(3)　1632-1652　2025/08/01
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI： 10.1137/24m1696093 　

eISSN： 1936-4954
Two extremum problems for Neumann eigenvalues Peer-reviewed

Lorenzo Cavallina, Kei Funano, Antoine Henrot, Antoine Lemenant, Ilaria Lucardesi, Shigeru Sakaguchi

Journal d'Analyse Mathématique　155　(2)　657-697　2025/03/24
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s11854-025-0366-3 　

ISSN： 0021-7670

eISSN： 1565-8538
A miscellanea of qualitative and symmetry properties of the solutions to the two-phase Serrin's problem Invited Peer-reviewed

Lorenzo Cavallina

to appear in Shape Design Mathematics --- Proceedings of ``Symposium on Shape Design and Mathematics 2024'', Tohoku Series of Mathematical Science, Springer, arXiv:2411.00320arXiv:2411.00320　2024/11
Symmetry and asymmetry in a multi-phase overdetermined problem Peer-reviewed

Lorenzo Cavallina

Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications　26　(3)　473-488　2024/06
Publisher: European Mathematical Society - EMS - Publishing House GmbH
DOI： 10.4171/ifb/512 　

ISSN： 1463-9963

eISSN： 1463-9971
Nondegeneracy implies the existence of parametrized families of free boundaries Peer-reviewed

Lorenzo Cavallina

Journal of Differential Equations　383　1-23　2024/02
Publisher: Elsevier BV
DOI： 10.1016/j.jde.2023.11.011 　

ISSN： 0022-0396
Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems Peer-reviewed

Lorenzo Cavallina, Giorgio Poggesi

to appear in Indiana University Mathematics Journal (2025+) arXiv:2312.11088　2023/12
Why are the Solutions to Overdetermined Problems Usually “As Symmetric as Possible”? Peer-reviewed

Lorenzo Cavallina

The Journal of Geometric Analysis　34　(1)　2023/11/18
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s12220-023-01467-8 　

ISSN： 1050-6926

eISSN： 1559-002X

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Abstract In this paper, we study the symmetry properties of nondegenerate critical points of shape functionals using the implicit function theorem. We show that, if a shape functional is invariant with respect to some one-parameter group of rotations, then its nondegenerate critical points (bounded open sets with smooth enough boundary) share the same symmetries. We also consider the case where the shape functional exhibits translational invariance in addition to just rotational invariance. Finally, we study the applications of this result to the theory of one/two-phase overdetermined problems of Serrin-type. En passant, we give a simple proof of the fact that, under suitable smoothness assumptions, the ball is the only nondegenerate critical point of the Lagrangian associated to the maximization problem for the torsional rigidity under a volume constraint. We remark that the proof does not rely on either the method of moving planes or rearrangement techniques.
A characterization of a hyperplane in two-phase heat conductors Peer-reviewed

L. Cavallina, S. Sakaguchi, S. Udagawa

Communications in Analysis and Geometry　31　(7)　1867-1888　2023
Quantitative stability estimates for a two-phase Serrin-type overdetermined problem Peer-reviewed

Lorenzo Cavallina, Giorgio Poggesi, Toshiaki Yachimura

Nonlinear Analysis　222　112919-112919　2022/09
Publisher: Elsevier BV
DOI： 10.1016/j.na.2022.112919 　

ISSN： 0362-546X
The simultaneous asymmetric perturbation method for overdetermined free boundary problems Peer-reviewed

Lorenzo Cavallina

Nonlinear Analysis　215　112685-112685　2022/02
Publisher: Elsevier BV
DOI： 10.1016/j.na.2021.112685 　

ISSN： 0362-546X
Local analysis of a two phase free boundary problem concerning mean curvature Peer-reviewed

Lorenzo Cavallina

Indiana University Mathematics Journal　71　(4)　1411-1435　2022
Publisher: Indiana University Mathematics Journal
DOI： 10.1512/iumj.2022.71.9014 　

ISSN： 0022-2518
Symmetry breaking solutions for a two-phase overdetermined problem of Serrin-type Invited Peer-reviewed

Lorenzo Cavallina, Toshiaki Yachimura

Current Trends in Analysis, its Applications and Computation (Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019) Research Perspectives, Birkhäuser　433-441　2022
The Double Queen Dido’s Problem Peer-reviewed

Lorenzo Cavallina, Antoine Henrot, Shigeru Sakaguchi

The Journal of Geometric Analysis　31　(8)　7750-7772　2021/08
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s12220-020-00549-1 　

ISSN： 1050-6926

eISSN： 1559-002X
On an overdetermined problem for composite materials

Lorenzo Cavallina

RIMS Kokyuroku　2186　18-22　2021/06
Two-Phase Heat Conductors with a Surface of the Constant Flow Property Peer-reviewed

Lorenzo Cavallina, Rolando Magnanini, Shigeru Sakaguchi

The Journal of Geometric Analysis　31　(1)　312-345　2021/01
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s12220-019-00262-8 　

ISSN： 1050-6926

eISSN： 1559-002X
On a two-phase Serrin-type problem and its numerical computation Peer-reviewed

Lorenzo Cavallina, Toshiaki Yachimura

ESAIM: Control, Optimisation and Calculus of Variations　26　65-65　2020/09
Publisher: EDP Sciences
DOI： 10.1051/cocv/2019048 　

ISSN： 1292-8119

eISSN： 1262-3377

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We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of a perturbation argument relying on shape derivatives and the implicit function theorem. This problem is also treated numerically, by means of a steepest descent algorithm based on a Kohn–Vogelius functional.
Spontaneous symmetry breaking for a two-phase overdetermined problem of Serrin-type

Lorenzo Cavallina, Toshiaki Yachimura

Proceedings of the Conference on Computational Engineering and Science (CD-ROM)　25　2020/06
Stability analysis of the two-phase torsional rigidity near a radial configuration Peer-reviewed

Lorenzo Cavallina

Applicable Analysis　98　(10)　1889-1900　2019/07/27
Publisher: Informa UK Limited
DOI： 10.1080/00036811.2018.1478082 　

ISSN： 0003-6811

eISSN： 1563-504X
On a two-phase shape optimization problem and its related overdetermined problem

Lorenzo Cavallina

Proceedings of the Conference on Computational Engineering and Science　24　2019/05
On a two-phase overdetermined problem of Serrin type

Lorenzo Cavallina

Hokkaido University technical report series in mathematics　176　525-533　2019/03
The Homogenization Method for Topology Optimization of Structures: Old and New Invited Peer-reviewed

G. Allaire, L. Cavallina, N. Miyake, T. Oka, T. Yachimura

Interdisciplinary Information Sciences　25　(2)　75-146　2019
Publisher: Graduate School of Information Sciences, Tohoku University
DOI： 10.4036/iis.2019.b.01 　

ISSN： 1340-9050

eISSN： 1347-6157
A local analysis of the radial configuration for the two-phase torsion problem in the ball

Lorenzo Cavallina

RIMS Kokyuroku　2082　7-20　2018/08
Locally optimal configurations for the two-phase torsion problem in the ball Peer-reviewed

Lorenzo Cavallina

Nonlinear Analysis, Theory, Methods and Applications　162　33-48　2017/10/01
Publisher: Elsevier Ltd
DOI： 10.1016/j.na.2017.06.005 　

ISSN： 0362-546X
Local optimizer for the two-phase torsion problem in some symmetric domains

Lorenzo Cavallina

79-84　2016
Monotone valuations on the space of convex functions Peer-reviewed

L. Cavallina, A. Colesanti

Analysis and Geometry in Metric Spaces　3　(1)　167-211　2015
Publisher: De Gruyter Open Ltd
DOI： 10.1515/agms-2015-0012 　

ISSN： 2299-3274

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Presentations 53

Two extremum problems for Neumann eigenvalues Invited

Lorenzo Cavallina

Numerical methods for spectral problems: theory and applications, Miyakojima　2025/08/27
二相 Serrin 型優決定問題の解の幾何学的性質について Invited

Lorenzo Cavallina

第6回大同大学若手微分方程式セミナー in 宮崎, 宮崎大学　2025/08/20
「二相」を超えて— 無限相の場合を含む多相複合媒質における楕円型及び放物型優決定問題 Invited

Lorenzo Cavallina

Tohoku University Applied Analysis Seminar　2025/04/10
「二相」を超えて ― 無限相の場合を含む多相複合媒質における楕円型及び放物型優決定問題 Invited

Lorenzo Cavallina

第2回諏訪偏微分方程式研究集会, 長野県諏訪市駅前交流テラス「すわっチャオ」会議室　2025/03/05
A characterization of radial symmetry in composite media via overdetermined level sets

Lorenzo Cavallina (speaker), Giorgio Poggesi

2025/02/15
Beyond two-phase: elliptic and parabolic overdetermined problems in general multi-phase settings, including potentially infinite phases Invited

Lorenzo Cavallina

The 42th Kyushu Symposium on Partial Differential Equations, Kyushu University　2025/01/27
Local well-posedness of shape flows with regularization (in Japanese) Invited

Lorenzo Cavallina

JSIAM, [正会員 OS] かたちの数理とその応用, Kyoto University　2024/09/16
二相Serrin型優決定問題について Invited

Lorenzo Cavallina

形状設計数学シンポジウム2024　2024/09/03
A characterization of radial symmetry for composite media by overdetermined level sets Invited

Lorenzo Cavallina

First Chinese-Italian Workshop on Elliptic PDEs and Variational Problems, Huangshan University　2024/06/06
Characterizing radial symmetry via the knowledge of "special" level sets Invited

Lorenzo Cavallina

2024/04/30
The study of shape optimization problems and overdetermined problems by means of shape derivatives Invited

Lorenzo Cavallina

2024/04/30
形状汎関数を用いた「かたち」と「うごき」の研究 Invited

Lorenzo Cavallina

数学と諸分野の連携に向けた若手数学者交流会 (YMC) 2024　2024/03/12
A characterization of radial symmetry for composite media by overdetermined level sets Invited

Lorenzo Cavallina

UWA Analysis Seminar, University of Western Australia　2024/02/20
A characterization of radial symmetry for composite media by overdetermined level sets Invited

Lorenzo Cavallina

Geometric PDE and Applied Analysis Seminar, OIST　2024/02/09
等位集合における優決定条件を用いた複合媒質の球対称性の特徴づけ Invited

Lorenzo Cavallina

Kansai University, Probability and related topics 2024　2024/02/01
How to characterize radial symmetry in two-phase conductors by overdetermined conditions on the level sets of the torsion function Invited

Lorenzo Cavallina

Mt. Aoba Analysis and Geometry miniworkshop, 東北大学　2024/01/24
How much overdetermination is enough to get symmetry in two-phase problems Invited

Lorenzo Cavallina

2024 Japan-Korea Workshop on Nonlinear PDEs and Its Applications, 広島大学　2024/01/16
Face 2-phase: how much overdetermination is enough to get symmetry in multi-phase problems Invited

Lorenzo Cavallina

Non linear analysis seminar, one day workshop, Keio University　2023/11/24
Symmetry and asymmetry in a multiphase overdetermined problem Invited

Lorenzo Cavallina

Homogenization and/or nonlocal operators　2023/08/08
On symmetry and asymmetry in a multi-phase overdetermined problem Invited

Lorenzo Cavallina

2023/04/28
多相優決定問題における対称性と非対称性について Invited

Lorenzo Cavallina

2023/04/24
On an overdetermined problem in a composite medium

Lorenzo Cavallina

7th camp Homogenization and its related topics (Tohoku University)　2023/03/27
On an overdetermined problem of Serrin-type in a two-phase composite medium with imperfect interfaces Invited

Lorenzo Cavallina

Kyoto University Applied Mathematics Seminar (together with "AIMR Math Group seminar")　2023/01/20
On an overdetermined problem in two-phase composite media with imperfect interfaces Invited

Lorenzo Cavallina

2022/12/25
On the symmetry and asymmetry for nondegenerate critical points of shape functionals Invited

Lorenzo Cavallina

2022/06/18
On the families of solutions to an overdetermined problem in composite media Invited

Lorenzo Cavallina

Saga Workshop on Partial Differential Equations　2022/03/07
The construction of a parametrized family solutions to some overdetermined problems

Lorenzo Cavallina

2021/10/09
A two-phase free boundary problem concerning mean curvature

Lorenzo Cavallina

Workshop for young scholars: Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods -　2021/09/02
On an overdetermined problem for composite materials

Lorenzo Cavallina

RIMS Workshop on Recent developments on inverse problems for partial differential equations and their applications　2021/01/06
優決定問題における同時非対称摂動法 Invited

Lorenzo Cavallina

2020/10/08
Bifurcation analysis for a two-phase overdetermined problem of Serrin type Invited

Lorenzo Cavallina, Toshiaki Yachimura

日本応用数理学会2020 年年会D[研究部会OS] 数理設計(Zoom)　2020/09/10
On two different two-phase overdetermined problems

Lorenzo Cavallina

Fukuoka University Analysis Seminar　2020/07/31
Local behavior near the trivial solutions of some two-phase elliptic overdetermined problems Invited

Lorenzo Cavallina

UWA Zoom Analysis Seminar　2020/07/15
The characterization of an interface with constant temperature in two-phase heat conductors

Lorenzo Cavallina, Shigeru Sakaguchi, Seiichi Udagawa

MSJ Spring Meeting 2020 at Nihon University　2020/03
On a two-phase isoperimetric problem

Lorenzo Cavallina, Antoine Henrot, Shigeru Sakaguchi

MSJ Spring Meeting 2020 at Nihon University　2020/03
On an overdetermined problem for composite materials Invited

Lorenzo Cavallina

Mini-Workshop “Mathematical Physics and PDEs　2019/11/15
On a shape optimization problem for composite materials and its related overdetermined problem Invited

Lorenzo Cavallina

RIMS Workshop “Pattern formation and defects in biology and materials science　2019/10/09
The double queen Dido’s problem Invited

Lorenzo Cavallina

Workshop Lorraine-Tohoku　2019/09/18
On the pairs of domains that solve a two-phase overdetermined problem of Serrin-type

Lorenzo Cavallina

12th ISAAC Congress, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs　2019/07/30
On a variation of Serrin’s overdetermined problem in a two-phase setting: the geometry of non-trivial solutions Invited

Lorenzo Cavallina

RIMS Workshop "Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics"　2019/07/19
On a two-phase shape optimization problem and its related overdertermined problem

Lorenzo Cavallina

24th conference of the Japan Society for Computational Engineering and Science　2019/05/31
On a two-phase overdetermined problem of Serrin type and its numerical computation

Lorenzo Cavallina, Toshiaki Yachimura

MSJ Spring Meeting 2019 at Tokyo Institute of Technology　2019/03/17
On a two-phase overdetermined problem of Serrin type

Lorenzo Cavallina

The 15th Mathematics Conference for Young Researchers　2019/03/06
On a two-phase overdetermined problem: from a theoretical and numerical point of view Invited

Lorenzo Cavallina

The 20th Northeastern Symposium on Mathematical Analysis　2019/02/19
Local analysis of the torsional rigidity of a two-phase body under general perturbations Invited

Lorenzo Cavallina

Workshop on Nonlinear Partial Differential Equations – Japan-China Joint Project for Young Mathematicians 2018　2018/10/26
The study of the two-phase torsion problem by means of shape derivatives Invited

Lorenzo Cavallina

Joint Firenze-Tohoku Research Workshop on Nonlinear PDEs　2018/10/22
On the geometrical shape of two-phase heat conductors with a surface of the constant flow property

Lorenzo Cavallina, Rolando Magnanini, Shigeru Sakaguchi

MSJ Spring Meeting 2018 at the Univeristy of Tokyo　2018/03/20
On the shape of a two-phase heat conductor satisfying the constant flow property at the boundary Invited

Lorenzo Cavallina

15th Aoba-yama PDE Seminar “PDEs and Inverse Problems”　2018/02/22
On the spherically symmetric solutions to the two-phase torsional rigidity optimization problem

Lorenzo Cavallina

MSJ Autumn Meeting 2017, at Yamagata University　2017/09/11
Local optimality of radially symmetric configurations for the two-phase torsion problem in the ball Invited

Lorenzo Cavallina

RIMS workshop “Analysis on Shapes of Solutions to Partial Differential Equations”　2017/06/05
Locally optimal configurations for the two-phase torsion problem in the ball Invited

Lorenzo Cavallina

Matsuyama Analysis Seminar 2017　2017/02/03
Local optimizers for the two-phase torsion problem in a ball Invited

Lorenzo Cavallina

Geometry of solutions of PDE’s and its related inverse problems — A conference in honor of Professor Shigeru Sakaguchi’s sixtieth birthday —　2016/10/05
Locally optimal configurations for the two-phase torsion problem in some symmetric domains

Lorenzo Cavallina

第38回発展方程式若手セミナー　2016/08/29

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Research Projects 5

Quantitative analysis for nonlinear evolution equations of diffusion type

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))

Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))

Institution: Tohoku University

2021/10 - 2027/03
On an overdetermined problem for composite materials

Lorenzo Cavallina

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists

Category: Grant-in-Aid for Early-Career Scientists

Institution: Tohoku University

2022/04 - 2026/03
The study of "Shape" and "Motion" by means of shape functionals

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Transformative Research Areas (A)

Institution: Tohoku University

2023/04 - 2025/03
Analysis of a two-phase overdetermined problem of Serrin type: from local to global

Lorenzo Cavallina

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up

Category: Grant-in-Aid for Research Activity Start-up

Institution: Tohoku University

2020/09 - 2022/03
複合媒質における新しいSerrin型優決定問題

Cavallina Lorenzo

Offer Organization: 日本学術振興会

System: 科学研究費助成事業特別研究員奨励費

Category: 特別研究員奨励費

Institution: 東北大学

2018/04 - 2020/03

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研究目的は複合媒質における放物型及び楕円型優決定問題の解の幾何学的性質を明らかにすることであった。主な研究成果は二つある. ① 論文L.Cavallina, T.Yachimura, "On a two-phase Serrin-type problem and its numerical computation" ではSerrinの優決定問題の一般化としての複合媒質に関する二相円型優決定問題を考えた。二つの相における伝導率の比が「臨界値」でない場合、同心球でない解（非自明解）もまた存在することを上述の論文で示した。伝導率の比が「臨界値」の場合は、論文L. Cavallina, T. Yachimura, "Symmetry breaking solutions for a two-phase overdetermined problem of Serrin-type", (Research Perspective series of Birkhauserに掲載決定)で解析された。伝導率の比がcritical valueの時、Crandall-Rabinowitzの定理を用いることによって、対称性の自発的破れが起こることを示した。主結果をより詳しく述べると、介在物が球のときの回転対称でない解の存在を示した。 ② ユークリッド空間上で二相熱方程式におけるコーシー問題を考える。ここで各相における熱伝導率が異なり、初期温度がそれぞれ0と1とする。さらに界面が一様にC^6級とする。このとき、時間と位置にも依存しない、一定の温度を持つ界面は超平面に限る。この結果を論文L.Cavallina,S.Sakaguchi,S.Udagawa,"A characterization of a hyperplane in two-phase heat conductors"(投稿中)で示した。

Social Activities 1

形状最適化と形状の微分

高校生のための仙台数学セミナー

2023/07/31 - 2023/08/02