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 .
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1156,
author = {Dominik Mielczarek and Jerzy Rydlewski and Ewa Szlachtowska},
title = {On the solvability of Dirichlet problem for the weighted p-Laplacian},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {34},
year = {2014},
pages = {89-103},
zbl = {1328.35057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1156}
}
Dominik Mielczarek; Jerzy Rydlewski; Ewa Szlachtowska. On the solvability of Dirichlet problem for the weighted p-Laplacian. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 34 (2014) pp. 89-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1156/
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