Wiener's criterion for the unique solvability of the Dirichlet problem in arbitrary open sets with non-compact boundaries

DOI10.1016/j.na.2006.06.004zbMath1134.35029OpenAlexW2094712741MaRDI QIDQ880319

Ugur G. Abdulla

Publication date: 15 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.06.004

zbMATH Keywords

Dirichlet problemuniquenessharmonic functionunbounded domainLaplace equationremovable singularitysingular Dirichlet problemnon-compact boundaryWiener's criterionirregularity of infinityregularity of infinity

Mathematics Subject Classification ID

Brownian motion (60J65) Axiomatic potential theory (31D05) Probabilistic potential theory (60J45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Potentials and capacities on other spaces (31C15)

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Cites Work

• Diffusion processes and their sample paths.
• Potentials and the random walk
• Lectures on potential theory. 2nd ed., revised and enlarged
• On the solvability and stability of the Dirichlet problem
• Sur le rôle du point à l'infini dans la théorie des fonctions harmoniques
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