Geodesic
On the solvability of Dirichlet problem for the weighted p-Laplacian
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 1, pp. 89-103.

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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 W₀^1,p(Ω).
Keywords: weighted p-Laplacian, weak solutions, solvability, semi-inner product spaces 
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Mielczarek, Dominik; Rydlewski, Jerzy; Szlachtowska, Ewa. On the solvability of Dirichlet problem for the weighted p-Laplacian. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 1, pp. 89-103. http://geodesic.mathdoc.fr/item/DMDICO_2014_34_1_a4/

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