Gradient Estimates in Fractional Dirichlet Problems

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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Veröffentlicht in:Potential analysis 2021-04, Vol.54 (4), p.627-636
Hauptverfasser: Fall, Mouhamed Moustapha, Jarohs, Sven
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Dirichlet problem
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
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Beschreibung
Zusammenfassung: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.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-020-09842-8