Gradient Estimates in Fractional Dirichlet Problems

We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such solutions near the boundary of the underlying domain.

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Bibliographic Details
Published inPotential analysis Vol. 54; no. 4; pp. 627 - 636
Main Authors Fall, Mouhamed Moustapha, Jarohs, Sven
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2021
Springer Nature B.V
Subjects
Boundary conditions
Dirichlet problem
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
35B65
Boundary regularity
47G20
Fractional Laplacian
Online AccessGet full text
ISSN0926-2601
1572-929X
DOI10.1007/s11118-020-09842-8

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Summary:We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such solutions near the boundary of the underlying domain.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-020-09842-8