Optimization results for the higher eigenvalues of the p‐Laplacian associated with sign‐changing capacitary measures
2021
In this paper we prove the existence of an optimal set for the minimization of the $k$-th variational eigenvalue of the $p$-Laplacian among $p$-quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the $p$-Laplacian associated with Schrodinger 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 $p$-Laplacian associated with sign-changing capacitary measures under $\gamma$-convergence.
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
26
References
4
Citations
NaN
KQI