The Wiener Criterion for Nonlocal Dirichlet Problems

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability s ∈ ( 0 , 1 ) and summability p > 1 . We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the...

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Bibliographic Details
Published in:	Communications in mathematical physics 2023-06, Vol.400 (3), p.1961-2003
Main Authors:	Kim, Minhyun, Lee, Ki-Ahm, Lee, Se-Chan
Format:	Article
Language:	eng
Subjects:	Classical and Quantum Gravitation Complex Systems Criteria Differential equations Dirichlet problem Mathematical and Computational Physics Mathematical Physics Operators (mathematics) Physics Physics and Astronomy Potential theory Quantum Physics Relativity Theory Theoretical
Online Access:	Get full text
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Summary:	We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability s ∈ ( 0 , 1 ) and summability p > 1 . We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.
ISSN:	0010-3616 1432-0916