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Existence of a renormalized solution of nonlinear degenerate elliptic problems

Volume 41 / 2014

Youssef Akdim, Chakir Allalou Applicationes Mathematicae 41 (2014), 131-140 MSC: Primary 35J70; Secondary 35J85. DOI: 10.4064/am41-2-1

Abstract

We study a general class of nonlinear elliptic problems associated with the differential inclusion $\beta (u)-{\rm div}(a(x,Du)+F(u))\ni f $ in $\varOmega $ where $f\in L^{\infty }(\varOmega )$. The vector field $a(\cdot ,\cdot )$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general $L^\infty $-data.

Authors

  • Youssef AkdimLIMAO, Faculté Polydisciplinaire
    B.P. 1223 Taza Gare, Taza, Morocco
    e-mail
  • Chakir AllalouLIMAO, Faculté Polydisciplinaire
    B.P. 1223 Taza, Gare Taza, Marocco
    e-mail

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