Given two isotropic homogeneous materials represented by two constants
Mots-clés : Two-phase material, Control in the coefficients, Eigenvalue, Non-existence
@article{AIHPC_2017__34_5_1215_0, author = {Casado-D{\'\i}az, Juan}, title = {A characterization result for the existence of a two-phase material minimizing the first eigenvalue}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1215--1226}, publisher = {Elsevier}, volume = {34}, number = {5}, year = {2017}, doi = {10.1016/j.anihpc.2016.09.006}, zbl = {1379.49044}, mrnumber = {3742521}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2016.09.006/} }
TY - JOUR AU - Casado-Díaz, Juan TI - A characterization result for the existence of a two-phase material minimizing the first eigenvalue JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1215 EP - 1226 VL - 34 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2016.09.006/ DO - 10.1016/j.anihpc.2016.09.006 LA - en ID - AIHPC_2017__34_5_1215_0 ER -
%0 Journal Article %A Casado-Díaz, Juan %T A characterization result for the existence of a two-phase material minimizing the first eigenvalue %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1215-1226 %V 34 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2016.09.006/ %R 10.1016/j.anihpc.2016.09.006 %G en %F AIHPC_2017__34_5_1215_0
Casado-Díaz, Juan. A characterization result for the existence of a two-phase material minimizing the first eigenvalue. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1215-1226. doi : 10.1016/j.anihpc.2016.09.006. https://www.numdam.org/articles/10.1016/j.anihpc.2016.09.006/
[1] Optimization problems with prescribed rearrangements, Nonlinear Anal. TMA, Volume 13 (1989), pp. 185–220 | DOI | MR | Zbl
[2] Shape Optimization by the Homogenization Method, Appl. Math. Sci., vol. 146, Springer-Verlag, New York, 2002 | DOI | MR | Zbl
[3] A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl., Volume 36 (1957), pp. 235–249 | MR | Zbl
[4] Sur un problème d'unicité pour les systèmes d'équations aux dérivées partielles à deux variables indépendantes, Ark. Mat. Astron. Fys., Volume 26 (1939), pp. 1–9 | JFM | MR | Zbl
[5] Some smoothness results for the optimal design of a two-composite material which minimizes the energy, Calc. Var. Partial Differ. Equ., Volume 53 (2015), pp. 649–673 | DOI | MR | Zbl
[6] Smoothness properties for the optimal mixture of two isotropic materials. The compliance and eigenvalue problems, SIAM J. Control Optim., Volume 53 (2015), pp. 2319–2349 | DOI | MR | Zbl
[7] Relaxation of a control problem in the coefficients with a functional of quadratic growth in the gradient, SIAM J. Control Optim., Volume 47 (2008), pp. 1428–1459 | DOI | MR | Zbl
[8] Minimization of the ground state for two phase conductors in low contrast regime, SIAM J. Appl. Math., Volume 72 (2012), pp. 1238–1259 | DOI | MR | Zbl
[9] An extremal eigenvalue problem for a two-phase conductor in a ball, Appl. Math. Optim., Volume 60 (2009) no. 2, pp. 173–184 | DOI | MR | Zbl
[10] Topology, Wm. C. Brown Publishers, Dubuque, 1966
[11] Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992 | MR | Zbl
[12] Geometric Measure Theory, Springer-Verlag, New York, 1969 | MR | Zbl
[13] Differential Topology, Prentice-Hall, Englewood Cliffs, 1974 | MR | Zbl
[14] Numerical study of a relaxed variational problem for optimal design, Comput. Methods Appl. Mech. Eng., Volume 57 (1986), pp. 107–127 | DOI | MR | Zbl
[15] Analysis and numerical studies of a problem of shape design, Arch. Ration. Mech. Anal., Volume 114 (1991), pp. 343–363 | DOI | MR | Zbl
[16] Optimal ground state energy of two phase conductors, Electron. J. Differ. Equ., Volume 171 (2014), pp. 1–8 | MR | Zbl
[17] Un contre-exemple pour le problème du contrôle dans les coefficients, C. R. Acad. Sci. Paris A, Volume 273 (1971), pp. 708–711 | MR | Zbl
[18] Théorèmes de non existence pour des problèmes de contrôle dans les coefficients, C. R. Acad. Sci. Paris A, Volume 274 (1972), pp. 395–398 | MR | Zbl
[19] Calcul des variations et homogénéisation, Les méthodes de l'homogénéisation: theorie et applications en physique, Eirolles, Paris, 1985, pp. 319–369
[19] Progress in Nonlinear Diff. Equ. and Their Appl., vol. 31, Birkaüser, Boston, 1998, pp. 139–174 (English translation Calculus of variations and homogenization Topics in the Mathematical Modelling of Composite Materials)
[20] Global minimizer of the ground state for two phase conductors in low contrast regime, ESAIM Control Optim. Calc. Var., Volume 20 (2014) no. 2, pp. 362–388 | Numdam | MR | Zbl
[21] A symmetry problem in potential theory, Arch. Ration. Mech. Anal., Volume 43 (1971), pp. 304–318 | DOI | MR | Zbl
[22] Remarks on optimal design problems, Calculus of Variations, Homogenization and Continuous Mechanics, Adv. Math. Appl. Sci., vol. 18, World Scientific, Singapore, 1994, pp. 279–296
[23] The General Theory of Homogenization. A Personalized Introduction, Springer, Berlin Heidelberger, 2009 | MR | Zbl
- Optimal design problems through the homogenization method, Numerical Control: Part B, Volume 24 (2023), p. 1 | DOI:10.1016/bs.hna.2022.10.003
- Spectral Optimization of Inhomogeneous Plates, SIAM Journal on Control and Optimization, Volume 61 (2023) no. 2, p. 852 | DOI:10.1137/21m1435203
- The Maximization of the First Eigenvalue for a Two-Phase Material, Applied Mathematics Optimization, Volume 86 (2022) no. 1 | DOI:10.1007/s00245-022-09825-8
- Shape Optimization of a Weighted Two-Phase Dirichlet Eigenvalue, Archive for Rational Mechanics and Analysis, Volume 243 (2022) no. 1, p. 95 | DOI:10.1007/s00205-021-01726-4
- Minimization of the p-Laplacian first eigenvalue for a two-phase material, Journal of Computational and Applied Mathematics, Volume 399 (2022), p. 113722 | DOI:10.1016/j.cam.2021.113722
- Some comparison results and a partial bang-bang property for two-phases problems in balls, Mathematics in Engineering, Volume 5 (2022) no. 1, p. 1 | DOI:10.3934/mine.2023010
- Optimality Conditions and Numerical Resolution, Optimal Design of Multi-Phase Materials (2022), p. 43 | DOI:10.1007/978-3-030-98191-4_3
- An optimal design problem for a two-phase isolating material in the wall of a cavity, Nonlinear Analysis, Volume 200 (2020), p. 112025 | DOI:10.1016/j.na.2020.112025
- Minimization of the First Nonzero Eigenvalue Problem for Two-Phase Conductors with Neumann Boundary Conditions, SIAM Journal on Applied Mathematics, Volume 80 (2020) no. 4, p. 1607 | DOI:10.1137/19m1251709
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