Existence and uniqueness of solutions for degenerate nonlinear elliptic equations in weigthed Sobolev spaces |
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| Author |
accava@gmail.com
Department of Mathematics, State University of Londrina, Brazil
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| Abstract |
In this paper we are interested in the existence and uniqueness of
solutions for the Dirichlet problem associated to the degenerate
nolinear elliptic equation
\begin{equation*}
-\sum_{j=1}^n D_j{\bigl[}{\cal A}_j(x, {\nabla}u)\,
{\omega}_2(x){\bigr]} + b(x, u)\,{\omega}_1(x) +
g(x)\,u(x)\\
= f_0(x) - \sum_{j=1}^nD_jf_j(x) \ \ {\rm on } \ \ {\Omega}
\end{equation*}
in the setting of the weighted Sobolev spaces ${\rm
W}_0^{1,p}(\Omega , {\omega}_1,{\omega}_2)$.
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| Keywords |
nonlinear degenerate elliptic equation; weighted Sobolev space
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| DOI |
doi:10.15330/ms.45.2.182-193
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| Reference |
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| Pages |
182-193
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| Volume |
45
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| Issue |
2
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
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