Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

Cavalheiro, Albo Carlos

doi:10.2478/mjpaa-2019-0012

Abstract

In this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations

${\begin{matrix} - div [𝒜 (x, \nabla u) ω_{1} + 𝒝 (x, u, \nabla u) ω_{2}] = f_{0} (x) - \sum_{j = 1}^{n} D_{j} f_{j} (x) in Ω, \\ u (x) = 0 on \partial Ω, \end{matrix}$ \left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.

in the setting of the weighted Sobolev spaces.

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Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

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