Optimization results for the higher eigenvalues of the p-Laplacian associated with sign-changing capacitary measures

Marco Degiovanni, Dario Cesare Severo Mazzoleni

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

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 originaleEnglish
pagine (da-a)97-146
Numero di pagine50
RivistaJournal of the London Mathematical Society
Volume104
DOI
Stato di pubblicazionePubblicato - 2021

Keywords

  • Capacitary measures

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