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Quantitative estimates on localized finite differences for the fractional poisson problem, and applications to regularity and spectral stability.
Commun. Math. Sci. 16, 913-961 (2018)
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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.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Porous-medium Equations; Mu-transmission; Laplacian; Operators; Domains; Dirichlet; Sobolev; Spaces
ISSN (print) / ISBN 1539-6746
Quellenangaben Volume: 16, Issue: 4, Pages: 913-961
Publisher International Press
Publishing Place Somerville, Mass.
Institute(s) Institute of Computational Biology (ICB)