L∞ bounds of Steklov eigenfunctions and spectrum stability under domain variation

[摘要] We give a practical tool to control the L-infinity-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. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-05