A Faber-Krahn inequality for mixed local and nonlocal operators

Abstract

We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost attain the minimum.

arXiv commentJournal d'Analyse Mathématique