Maximal and minimal norm of Laplacian eigenfunctions in a given subdomain*
Pedro R. S. Antunes · Inverse Problems · 2016
Abstract It is well known that for some planar domains, some of the Laplacian eigenfunctions are localized in a small region of the domain and decay rapidly outside this region. We address a shape optimization problem of minimizing or maximizing the L 2 norm of the eigenfunctions in some subdomains. This problem is solved by a numerical method involving the method of fundamental solutions and Hadamard shape derivatives. We use the adjoint method for a fast calculation of the shape gradient. Several numerical simulations illustrate the good performance of the method.