Opuscula Math. 32, no. 4 (2012), 775-781

Opuscula Mathematica

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

Ewa Szlachtowska

Abstract. The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \(p\)-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.

Keywords: \(p\)-Laplacian, weak solutions, solvability.

Mathematics Subject Classification: 35A15, 35J20, 35J60.

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  • Ewa Szlachtowska
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland.
  • Received: 2011-05-11.
  • Revised: 2012-03-19.
  • Accepted: 2012-03-20.
Opuscula Mathematica - cover

Cite this article as:
Ewa Szlachtowska, On the solvability of Dirichlet problem for the weighted p-Laplacian, Opuscula Math. 32, no. 4 (2012), 775-781, http://dx.doi.org/10.7494/OpMath.2012.32.4.775

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