Stability results for some fully nonlinear eigenvalue estimates

Abstract

In this paper, we give some stability estimates for the Faber–Krahn inequality relative to the eigenvalue λk(Ω) of the Hessian operator Sk, 1 ≤ k ≤ n, in a reasonable bounded domain Ω. Roughly speaking, we prove that if λk(Ω) is near to λk(B), where B is a ball which preserves an appropriate measure of Ω, then, in a suitable sense, Ω is close to B.