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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| Vydané v: | Nonlinear analysis Ročník 202; s. 112134 |
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01.01.2021
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| Abstract | 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. |
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| AbstractList | 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. We study a mixed boundary value problem for the p-Laplace equation Delta(p)u = 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. (C) 2020 TheAuthor(s). Published by Elsevier Ltd. |
| ArticleNumber | 112134 |
| Author | Björn, Jana Mwasa, Abubakar |
| Author_xml | – sequence: 1 givenname: Jana surname: Björn fullname: Björn, Jana email: jana.bjorn@liu.se organization: Department of Mathematics, Linköping University, SE 581 83, Linköping, Sweden – sequence: 2 givenname: Abubakar surname: Mwasa fullname: Mwasa, Abubakar email: abubakar.mwasa@liu.se organization: Department of Mathematics, Linköping University, SE 581 83, Linköping, Sweden |
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| Keywords | secondary Existence of weak solutions Mixed boundary value problem Capacity p-Laplace equation Wiener criterion Boundary regularity Unbounded cylinder primary Dirichlet and Neumann data |
| Language | English |
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| Snippet | 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... We study a mixed boundary value problem for the p-Laplace equation Delta(p)u = 0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary... |
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| SubjectTerms | [formula omitted]-Laplace equation Boundary regularity Capacity Dirichlet and Neumann data Existence of weak solutions Mixed boundary value problem Unbounded cylinder Wiener criterion |
| Title | Mixed boundary value problem for p-harmonic functions in an infinite cylinder |
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