A Faber-Krahn inequality for mixed local and nonlocal operators

2021/04/02 by Biagi, Stefano, Dipierro, Serena, Valdinoci, Enrico +1 · 6 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.00830

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.

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