J. Nonl. Evol. Equ. Appl. 2015 (7), pp. 105-119, published on July 20, 2016:

Renormalized solutions of Stefan degenerat elliptic nonlinear problems with variable exponent

Y. Akdim, C. Allalou

Sidi Mohamed Ben Abdellah University, Laboratory LSI, Poly-Disciplinary Faculty of Taza P.O. Box 1223, Taza Gare, Morocco

Received on March 21, 2015, revised version on July 15, 2015
Accepted on July 15, 2015

Communicated by Hui-Sheng Ding

Abstract.  In this paper, we study a general class of nonlinear elliptic degenerate problems associated with the differential inclusion
β(u)−div(a(x, Du)+F(u)) ∋ f in Ω where f ∈ L(Ω).
Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general L-data.
Keywords:Weighted variable exponent Sobolev spaces, truncations, degenerated elliptic operators.
2010 Mathematics Subject Classification:   35J15, 35J70, 35J85.

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