Entropy solutions for nonlinear elliptic equations with measure data and without strict monotonocity condition

Authors

  • Mohamed Rhoudaf
  • Y Akdim
  • E. Azroul

Keywords:

T-solution, boundary value problems, truncations, Weighted Sobolev Space

Abstract

We prove some existence results for nonlinear degenerated elliptic
problems of the form $$Au + g(x,u)= f-\mbox{div} F,$$ where $A(u) =
-\mbox{div}a(x,u,\nabla u)$ is a Leray-Lions, operator defined form
the weighted Sobolev space $W_0^{1,p}(\Omega,w)$ into its dual. The
right hand side, \ \ $f \in L^1(\Omega)$ and $ F \in {\displaystyle
\prod_{i=1}^N}L^{p'}(\Omega,w_i^*)$. Note that the Caracth\'eodory
function $a(x,s,\xi)$ satisfies only the large monotonicity instead
of the monotonicity strict condition. We overcome this difficulty by
using the $L^1$-version of Minty's lemma.

Author Biographies

  • Mohamed Rhoudaf
    Départementde Mathématiques et Informatique Faculté des Sciences Dhar-Mahraz, B.P1796 AtlasFès, Morocco
  • Y Akdim
    Faculté Poly-disciplinaire de Taza, B.P638 Taza, Maroc
  • E. Azroul
    Faculté Poly-disciplinaire de Taza, B.P638 Taza, Maroc

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Published

2009-03-22

Issue

Section

Partial Differential Equations and Dynamical Systems

How to Cite

Entropy solutions for nonlinear elliptic equations with measure data and without strict monotonocity condition. (2009). European Journal of Pure and Applied Mathematics, 1(4). https://www.ejpam.com/index.php/ejpam/article/view/100

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