Quantitative estimates on localized finite differences for the fractional poisson problem, and applications to regularity and spectral stability

Goro Akagi, Giulio Schimperna, Antonio Segatti, Laura V. Spinolo

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1 Citation (Scopus)

Abstract

We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the Lipschitz cone regularity condition. We then apply these estimates to obtain (i) regularity results for solutions of fractional Poisson problems in Besov spaces; (ii) quantitative stability estimates for solutions of fractional Poisson problems with respect to domain perturbations; (iii) quantitative stability estimates for eigenvalues and eigenfunctions of fractional Laplace operators with respect to domain perturbations.

Original languageEnglish
Pages (from-to)913-961
Number of pages49
JournalCommunications in Mathematical Sciences
Volume16
Issue number4
DOIs
Publication statusPublished - 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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