Existence of a renormalized solution of nonlinear degenerate elliptic problems

Youssef Akdim; Chakir Allalou

Applicationes Mathematicae, Volume 41 (2014), p. 131-140 / Harvested from The Polish Digital Mathematics Library

Abstract

We study a general class of nonlinear elliptic problems associated with the differential inclusion $β (u) - d i v (a (x, D u) + F (u)) ∋ f$ in Ω where $f \in L^{\infty} (Ω)$ . The vector field a(·,·) 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.

Published online : 2014-01-01

Zbl 1305.35066

EUDML-ID : urn:eudml:doc:280028

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     title = {Existence of a renormalized solution of nonlinear degenerate elliptic problems},
     journal = {Applicationes Mathematicae},
     volume = {41},
     year = {2014},
     pages = {131-140},
     zbl = {1305.35066},
     language = {en},
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Youssef Akdim; Chakir Allalou. Existence of a renormalized solution of nonlinear degenerate elliptic problems. Applicationes Mathematicae, Volume 41 (2014) pp. 131-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-1/