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ArticleOriginal scientific text

Title

On the solvability of Dirichlet problem for the weighted p-Laplacian

Authors 1, 1, 1

Affiliations

  1. AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space W₀1,p(Ω).

Keywords

ENG
weighted p-Laplacian, weak solutions, solvability, semi-inner product spaces

Bibliography

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2014/34/1
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Pages:
89-103
Main language of publication
English
Received
2014-01-31
Published
2014

DOI: 10.7151/dmdico1156

Exact and natural sciences