In this paper we prove the existence of an optimal set for the minimization of the (Formula presented.) th variational eigenvalue of the (Formula presented.) -Laplacian among (Formula presented.) -quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the (Formula presented.) -Laplacian associated with Schrödinger potentials. In order to deal with these nonlinear shape optimization problems, we develop a general approach which allows to treat the continuous dependence of the eigenvalues of the (Formula presented.) -Laplacian associated with sign-changing capacitary measures under (Formula presented.) -convergence.
|Number of pages||50|
|Journal||Journal of the London Mathematical Society|
|Publication status||Published - 2021|
- Capacitary measures