Artículo
A characterization result for the existence of a two-phase material minimizing the first eigenvalue
Autor/es | Casado Díaz, Juan |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2016-09-19 |
Fecha de depósito | 2022-11-10 |
Publicado en |
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Resumen | Given two isotropic homogeneous materials represented by two constants 0 <α< | |, we consider here the problem consisting in finding a mixture of these materials αχω + β(1 − χω), ω ⊂ RN measurable, with |ω| ≤ κ, such that ... Given two isotropic homogeneous materials represented by two constants 0 <α< | |, we consider here the problem consisting in finding a mixture of these materials αχω + β(1 − χω), ω ⊂ RN measurable, with |ω| ≤ κ, such that the first eigenvalue of the operator u ∈ H1 0 ( ) → −divαχω + β(1 − χω) ∇u reaches the minimum value. In a recent paper, [6], we have proved that this problem has not solution in general. On the other hand, it was proved in [1] that it has solution if is a ball. Here, we show the following reciprocate result: If ⊂ RN is smooth, simply connected and has connected boundary, then the problem has a solution if and only if is a ball. |
Cita | Casado Díaz, J. (2016). A characterization result for the existence of a two-phase material minimizing the first eigenvalue. Annales de l'Institut Henri Poincaré. Analyse non linéaire, 34 (5), 1215-1226. https://doi.org/10.1016/J.ANIHPC.2016.09.006. |
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