A characterization result for the existence of a two-phase material minimizing the first eigenvalue

  • Juan Casado-Díaz

    Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain

Abstract

Given two isotropic homogeneous materials represented by two constants in a smooth bounded open set , and a positive number , we consider here the problem consisting in finding a mixture of these materials , measurable, with , such that the first eigenvalue of the operator 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 is smooth, simply connected and has connected boundary, then the problem has a solution if and only if is a ball.

Cite this article

Juan Casado-Díaz, A characterization result for the existence of a two-phase material minimizing the first eigenvalue. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 5, pp. 1215–1226

DOI 10.1016/J.ANIHPC.2016.09.006