Calculus of Variations and Geometric Measure Theory

D. Bucur - A. Giacomini - P. Trebeschi

$L^\infty$ bounds of Steklov eigenfunctions and spectrum stability under domain variation

created by bucur on 01 Apr 2019


Submitted Paper

Inserted: 1 apr 2019
Last Updated: 1 apr 2019

Year: 2019


We give a practical tool to control the $L^\infty$-norm of the Steklov eigenfunctions in a Lipschitz domain in terms of the norm of the $BV$-trace operator. The norm of this operator has the advantage to be characterized by purely geometric quantities. As a consequence, we give a spectral stability result for the Steklov eigenproblem under geometric domain perturbations and several examples where stability occurs. In particular we deal with geometric domains which are not equi-Lipschitz, like vanishing holes, merging sets, approximations of inner peaks.