Optimization of shape for an elliptic system for mimimizaiton of the first eigenvalue (Q1374989)

The problem of determining a shape of a domain such that the first eigenvalue of the Laplace operator under the Dirichlet boundary conditions is minimal, is considered. The problem relates to the theory of optimization of shapes of objects with distributed parameters. An algorithm for approximate optimization of a shape is described, where the problem of evaluating an optimal domain is replaced by a family of problems of optimizing coefficients of an elliptic equation.