Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian

V. Gol'dshtein; V. V. Motreanu; A. Ukhlov

doi:10.1080/17476933.2011.555541

Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian

V. Gol'dshtein, V. V. Motreanu, A. Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.

Original language	English
Pages (from-to)	905-930
Number of pages	26
Journal	Complex Variables and Elliptic Equations
Volume	56
Issue number	10-11
DOIs	https://doi.org/10.1080/17476933.2011.555541
State	Published - 1 Oct 2011

Keywords

Dirichlet problems
Dirichlet spaces
Embedding properties
P-laplacian
Quasiconformal mappings
Weighted sobolev spaces

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2011.555541

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title = "Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian",

abstract = "We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.",

keywords = "Dirichlet problems, Dirichlet spaces, Embedding properties, P-laplacian, Quasiconformal mappings, Weighted sobolev spaces",

author = "V. Gol'dshtein and Motreanu, {V. V.} and A. Ukhlov",

note = "Funding Information: This work was partially supported by Israel Scientific Foundation (Grant No 1033/07). V.V. Motreanu was also supported by the Center for Advanced Studies in Mathematics of the Ben Gurion University of the Negev.",

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AU - Gol'dshtein, V.

AU - Motreanu, V. V.

AU - Ukhlov, A.

N1 - Funding Information: This work was partially supported by Israel Scientific Foundation (Grant No 1033/07). V.V. Motreanu was also supported by the Center for Advanced Studies in Mathematics of the Ben Gurion University of the Negev.

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Y1 - 2011/10/1

N2 - We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.

AB - We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.

KW - Dirichlet problems

KW - Dirichlet spaces

KW - Embedding properties

KW - P-laplacian

KW - Quasiconformal mappings

KW - Weighted sobolev spaces

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JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 10-11

ER -

Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian

Abstract

Keywords

ASJC Scopus subject areas

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