Mixed boundary value problem for p-harmonic functions in an infinite cylinder

We study a mixed boundary value problem for the p-Laplace equation Δpu=0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. Existence of weak solutions to the mixed problem is proved both for Sobole...

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Bibliographic Details
Published in:Nonlinear analysis Vol. 202; p. 112134
Main Authors: Björn, Jana, Mwasa, Abubakar
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.01.2021
Subjects:
[formula omitted]-Laplace equation
Boundary regularity
Capacity
Dirichlet and Neumann data
Existence of weak solutions
Mixed boundary value problem
Unbounded cylinder
Wiener criterion
secondary
Existence of weak solutions
Mixed boundary value problem
Capacity
p-Laplace equation
Wiener criterion
Boundary regularity
Unbounded cylinder
primary
Dirichlet and Neumann data
ISSN:0362-546X, 1873-5215, 1873-5215
Online Access:Get full text
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Summary:We study a mixed boundary value problem for the p-Laplace equation Δpu=0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. Existence of weak solutions to the mixed problem is proved both for Sobolev and for continuous data on the Dirichlet part of the boundary. We also obtain a boundary regularity result for the point at infinity in terms of a variational capacity adapted to the cylinder.
ISSN:0362-546X
1873-5215
1873-5215
DOI:10.1016/j.na.2020.112134