Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Improving the natural frequency of the CubeSat structure using voxel-based topology optimization method with the four-connected seed filling

Cong Wang, Changdong Zhang, Dawei Li, Tingting Liu and Wenhe Liao
Mechanics Based Design of Structures and Machines 53 (2) 1031 (2025)
https://doi.org/10.1080/15397734.2024.2381697

On numerical resolution of shape optimization bi-Laplacian eigenvalue problems

Abdelkrim Chakib, Ibrahim Khalil and Azeddine Sadik
Mathematics and Computers in Simulation 230 149 (2025)
https://doi.org/10.1016/j.matcom.2024.11.007

Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures

Harald Garcke, Paul Hüttl, Christian Kahle and Patrik Knopf
Applied Mathematics & Optimization 89 (1) (2024)
https://doi.org/10.1007/s00245-023-10093-3

A new numerical approach for solving shape optimization fourth-order spectral problems among convex domains

Abdelkrim Chakib and Ibrahim Khalil
Computers & Mathematics with Applications 149 171 (2023)
https://doi.org/10.1016/j.camwa.2023.09.001

Existence and regularity of optimal shapes for spectral functionals with Robin boundary conditions

Mickaël Nahon
Journal of Differential Equations 335 69 (2022)
https://doi.org/10.1016/j.jde.2022.07.001

Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization

Wei Gong, Jiajie Li and Shengfeng Zhu
SIAM Journal on Scientific Computing 44 (4) A2464 (2022)
https://doi.org/10.1137/21M1457400

A level set method for Laplacian eigenvalue optimization subject to geometric constraints

Meizhi Qian and Shengfeng Zhu
Computational Optimization and Applications 82 (2) 499 (2022)
https://doi.org/10.1007/s10589-022-00371-1

On accuracy of approximate boundary and distributed H1 shape gradient flows for eigenvalue optimization

Shengfeng Zhu, Xianliang Hu and Qingbiao Wu
Journal of Computational and Applied Mathematics 365 112374 (2020)
https://doi.org/10.1016/j.cam.2019.112374

Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization

Shengfeng Zhu, Xianliang Hu and Qifeng Liao
BIT Numerical Mathematics 60 (3) 853 (2020)
https://doi.org/10.1007/s10543-019-00782-3

Regularity for Shape Optimizers: The Degenerate Case

Dennis Kriventsov and Fanghua Lin
Communications on Pure and Applied Mathematics 72 (8) 1678 (2019)
https://doi.org/10.1002/cpa.21810

Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives

Shengfeng Zhu
Journal of Optimization Theory and Applications 176 (1) 17 (2018)
https://doi.org/10.1007/s10957-017-1198-9

On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate

Elvise Berchio, Davide Buoso and Filippo Gazzola
ESAIM: Control, Optimisation and Calculus of Variations 24 (1) 63 (2018)
https://doi.org/10.1051/cocv/2016076

Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint

B. Bogosel, A. Henrot and I. Lucardesi
SIAM Journal on Mathematical Analysis 50 (5) 5337 (2018)
https://doi.org/10.1137/17M1162147

A combined finite element and Bayesian optimization framework for shape optimization in spectral geometry

Sebastian Dominguez, Nilima Nigam and Bobak Shahriari
Computers & Mathematics with Applications 74 (11) 2874 (2017)
https://doi.org/10.1016/j.camwa.2017.08.044

Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

Pedro R. S. Antunes, Pedro Freitas and David Krejčiřík
Advances in Calculus of Variations 10 (4) 357 (2017)
https://doi.org/10.1515/acv-2015-0045

Numerical Minimization of Dirichlet Laplacian Eigenvalues of Four-Dimensional Geometries

Pedro R. S. Antunes and Édouard Oudet
SIAM Journal on Scientific Computing 39 (3) B508 (2017)
https://doi.org/10.1137/16M1083773

Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets

Dario Mazzoleni and Davide Zucco
ESAIM: Control, Optimisation and Calculus of Variations 23 (3) 869 (2017)
https://doi.org/10.1051/cocv/2016017

Computational Methods for Extremal Steklov Problems

Eldar Akhmetgaliyev, Chiu-Yen Kao and Braxton Osting
SIAM Journal on Control and Optimization 55 (2) 1226 (2017)
https://doi.org/10.1137/16M1067263

Maximising Neumann eigenvalues on rectangles

M. van den Berg, D. Bucur and K. Gittins
Bulletin of the London Mathematical Society 48 (5) 877 (2016)
https://doi.org/10.1112/blms/bdw049

Qualitative and Numerical Analysis of a Spectral Problem with Perimeter Constraint

Beniamin Bogosel and Édouard Oudet
SIAM Journal on Control and Optimization 54 (1) 317 (2016)
https://doi.org/10.1137/140999530

Optimisation of Eigenvalues of the Dirichlet Laplacian with a Surface Area Restriction

Pedro R. S. Antunes and Pedro Freitas
Applied Mathematics & Optimization 73 (2) 313 (2016)
https://doi.org/10.1007/s00245-015-9304-6

Blaschke–Santaló and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian

Dorin Bucur and Ilaria Fragalà
Proceedings of the London Mathematical Society 113 (3) 387 (2016)
https://doi.org/10.1112/plms/pdw032

The eigenvalues of the Laplacian with Dirichlet boundary condition in $$\mathbb {R}^2$$ R 2 are almost never minimized by disks

Amandine Berger
Annals of Global Analysis and Geometry 47 (3) 285 (2015)
https://doi.org/10.1007/s10455-014-9446-9

Lipschitz Regularity of the Eigenfunctions on Optimal Domains

Dorin Bucur, Dario Mazzoleni, Aldo Pratelli and Bozhidar Velichkov
Archive for Rational Mechanics and Analysis 216 (1) 117 (2015)
https://doi.org/10.1007/s00205-014-0801-6

Minimal Convex Combinations of Three Sequential Laplace-Dirichlet Eigenvalues

Braxton Osting and Chiu-Yen Kao
Applied Mathematics & Optimization 69 (1) 123 (2014)
https://doi.org/10.1007/s00245-013-9219-z

Minimal Dirichlet Energy Partitions for Graphs

Braxton Osting, Chris D. White and Édouard Oudet
SIAM Journal on Scientific Computing 36 (4) A1635 (2014)
https://doi.org/10.1137/130934568

Eigenvalues of polyharmonic operators on variable domains

Davide Buoso and Pier Domenico Lamberti
ESAIM: Control, Optimisation and Calculus of Variations 19 (4) 1225 (2013)
https://doi.org/10.1051/cocv/2013054

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian

Pedro Ricardo Simão Antunes, Pedro Freitas and James Bernard Kennedy
ESAIM: Control, Optimisation and Calculus of Variations 19 (2) 438 (2013)
https://doi.org/10.1051/cocv/2012016

Optimal spectral rectangles and lattice ellipses

Pedro R. S. Antunes and Pedro Freitas
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2150) 20120492 (2013)
https://doi.org/10.1098/rspa.2012.0492

Asymptotic behaviour of optimal spectral planar domains with fixed perimeter

Dorin Bucur and Pedro Freitas
Journal of Mathematical Physics 54 (5) (2013)
https://doi.org/10.1063/1.4803140

Minimal Convex Combinations of Sequential Laplace--Dirichlet Eigenvalues

Braxton Osting and Chiu-Yen Kao
SIAM Journal on Scientific Computing 35 (3) B731 (2013)
https://doi.org/10.1137/120881865

The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems

Carlos J. S. Alves and Pedro R. S. Antunes
SIAM Journal on Scientific Computing 35 (3) A1689 (2013)
https://doi.org/10.1137/110860380

Numerical Optimization of Low Eigenvalues of the Dirichlet and Neumann Laplacians

Pedro R. S. Antunes and Pedro Freitas
Journal of Optimization Theory and Applications 154 (1) 235 (2012)
https://doi.org/10.1007/s10957-011-9983-3

Optimal boundary holes for the Sobolev trace constant

Leandro Del Pezzo, Julián Fernández Bonder and Wladimir Neves
Journal of Differential Equations 251 (8) 2327 (2011)
https://doi.org/10.1016/j.jde.2011.07.006

On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian

Pedro R. S. Antunes and Antoine Henrot
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467 (2130) 1577 (2011)
https://doi.org/10.1098/rspa.2010.0444

On the inverse spectral problem for Euclidean triangles

Pedro R. S. Antunes and Pedro Freitas
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467 (2130) 1546 (2011)
https://doi.org/10.1098/rspa.2010.0540

An optimization problem for the first weighted eigenvalue problem plus a potential

Leandro Del Pezzo and Julián Bonder
Proceedings of the American Mathematical Society 138 (10) 3551 (2010)
https://doi.org/10.1090/S0002-9939-10-10384-0

Local minimizers of functionals with multiple volume constraints

Édouard Oudet and Marc Oliver Rieger
ESAIM: Control, Optimisation and Calculus of Variations 14 (4) 780 (2008)
https://doi.org/10.1051/cocv:2008013

Shape optimization problems for eigenvalues of elliptic operators

Z. Belhachmi, D. Bucur, G. Buttazzo and J.‐M. Sac‐Epée
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 86 (3) 171 (2006)
https://doi.org/10.1002/zamm.200510259