Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 318–343
Abstract
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $\beta(u)-div(a(x,Du)+F(u))\ni f$ in $\Omega $, where $f\in L^{1}(\Omega )$. A vector field $a(\cdot,\cdot)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general $L^1$-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2014.v30.n3.8
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 318–343
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Weighted Sobolev spaces Hardy inequality Truncations maximal monotone graph degenerated elliptic operators.
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