Abstract
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.
Lingua originale | English |
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pagine (da-a) | 97-146 |
Numero di pagine | 50 |
Rivista | Journal of the London Mathematical Society |
Volume | 104 |
DOI | |
Stato di pubblicazione | Pubblicato - 2021 |
Keywords
- Capacitary measures