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Title: Existence of entropy solutions for degenerate quasilinear elliptic equations in $L^1$ (English)
Author: Cavalheiro, Albo Carlos
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388
Volume: 22
Issue: 1
Year: 2014
Pages: 57-69
Summary lang: English
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Category: math
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Summary: In this article, we prove the existence of entropy solutions for the Dirichlet problem $$ (P)\begin {cases} -\mathrm{div} [{\omega }(x){\cal A} (x,u,{\nabla }u)]=f(x)-\mathrm{div} (G),&\text {in }\Omega \\ u(x) = 0,&\text {on }{\partial \Omega } \end {cases} $$ where $\Omega $ is a bounded open set of $\real ^N$, $N\geq 2$, $f \in L^1(\Omega )$ and $G/{\omega } \in [L^{p'}(\Omega , \omega )]^N$. (English)
Keyword: degenerate elliptic equations
Keyword: entropy solutions
Keyword: weighted Sobolev spaces
MSC: 35A01
MSC: 35J25
MSC: 35J60
MSC: 35J62
MSC: 35J70
idZBL: Zbl 1302.35180
idMR: MR3233727
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Date available: 2014-08-27T09:00:24Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/143906
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