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:
Édouard Oudet
ESAIM: COCV, 10 3 (2004) 315-330
Published online: 2004-06-15
This article has been cited by the following article(s):
58 articles
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
Shape optimization with virtual element method
Fang Feng, Hui Yang and Shengfeng Zhu Communications in Nonlinear Science and Numerical Simulation 131 107876 (2024) https://doi.org/10.1016/j.cnsns.2024.107876
Chiu-Yen Kao, Braxton Osting and Edouard Oudet 24 377 (2023) https://doi.org/10.1016/bs.hna.2022.08.001
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
Numerical Shape Optimization Among Convex Sets
Beniamin Bogosel Applied Mathematics & Optimization 87 (1) (2023) https://doi.org/10.1007/s00245-022-09920-w
Parametric shape optimization using the support function
Pedro R. S. Antunes and Beniamin Bogosel Computational Optimization and Applications 82 (1) 107 (2022) https://doi.org/10.1007/s10589-022-00360-4
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
Numerical calculation of extremal Steklov eigenvalues in 3D and 4D
Pedro R.S. Antunes Computers & Mathematics with Applications 104 50 (2021) https://doi.org/10.1016/j.camwa.2021.11.008
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
Extremal p -Laplacian eigenvalues
Pedro R S Antunes Nonlinearity 32 (12) 5087 (2019) https://doi.org/10.1088/1361-6544/ab47c5
Shifted lattices and asymptotically optimal ellipses
Richard S. Laugesen and Shiya Liu The Journal of Analysis 26 (1) 71 (2018) https://doi.org/10.1007/s41478-017-0070-5
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
Geometry of PDEs and Related Problems
Antoine Henrot Lecture Notes in Mathematics, Geometry of PDEs and Related Problems 2220 47 (2018) https://doi.org/10.1007/978-3-319-95186-7_2
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
Asymptotic Behaviour of Extremal Averages of Laplacian Eigenvalues
Pedro Freitas Journal of Statistical Physics 167 (6) 1511 (2017) https://doi.org/10.1007/s10955-017-1789-8
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
Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain
Pedro R S Antunes Inverse Problems 32 (11) 115003 (2016) https://doi.org/10.1088/0266-5611/32/11/115003
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
New Trends in Shape Optimization
Davide Buoso and Pier Domenico Lamberti International Series of Numerical Mathematics, New Trends in Shape Optimization 166 43 (2015) https://doi.org/10.1007/978-3-319-17563-8_3
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
Extremal eigenvalues of the Laplacian on Euclidean domains and closed surfaces
Bruno Colbois and Ahmad El Soufi Mathematische Zeitschrift 278 (1-2) 529 (2014) https://doi.org/10.1007/s00209-014-1325-3
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
Optimal Bilaplacian Eigenvalues
Pedro R. S. Antunes SIAM Journal on Control and Optimization 52 (4) 2250 (2014) https://doi.org/10.1137/130948860
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
Optimization of sums and quotients of Dirichlet–Laplacian eigenvalues
Pedro R.S. Antunes Applied Mathematics and Computation 219 (9) 4239 (2013) https://doi.org/10.1016/j.amc.2012.10.095
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
On the buckling eigenvalue problem
Pedro R S Antunes Journal of Physics A: Mathematical and Theoretical 44 (21) 215205 (2011) https://doi.org/10.1088/1751-8113/44/21/215205
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
About Hölder-regularity of the convex shape minimizing λ2
Jimmy Lamboley Applicable Analysis 90 (2) 263 (2011) https://doi.org/10.1080/00036811.2010.496361
Spectral optimization problems
Giuseppe Buttazzo Revista Matemática Complutense 24 (2) 277 (2011) https://doi.org/10.1007/s13163-011-0066-7
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
Optimization of spectral functions of Dirichlet–Laplacian eigenvalues
Braxton Osting Journal of Computational Physics 229 (22) 8578 (2010) https://doi.org/10.1016/j.jcp.2010.07.040
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
Mathematical analysis of the optimal habitat configurations for species persistence
Lionel Roques and François Hamel Mathematical Biosciences 210 (1) 34 (2007) https://doi.org/10.1016/j.mbs.2007.05.007
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