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Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

  • Abdelhafid SalmaniEmail author
  • Youssef Akdim
  • Hicham Redwane
Article
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Abstract

We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation
$$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$
where the right hand side \(\mu \) belongs to \(L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )\). The operator \(-\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) \) is a Leray–Lions anisotropic operator and \(\phi _{i} \in C^{0}({\mathbb {R}}, {\mathbb {R}})\).

Keywords

Entropy solutions Anisotropic elliptic equations Anisotropic Sobolev space 

Mathematics Subject Classification

35J60 35J87 35J66 

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, salmani abdelhafid as the corresponding author states that there is no conflict of interest.

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  • Abdelhafid Salmani
    • 1
    Email author
  • Youssef Akdim
    • 2
  • Hicham Redwane
    • 3
  1. 1.Laboratory LSI, Polydisciplinary Faculty of TazaSidi Mohamed ben Abdellah UniversityTazaMorocco
  2. 2.Laboratory LAMA Faculty of Sciences, Dhar-MahrezSidi Mohamed ben Abdellah UniversityFez AtlasMorocco
  3. 3.Faculty of Juridical, Economic and Social SciencesHassan 1st UniversitySettatMorocco

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