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arXiv · 2005.08383

Degenerate elliptic problem with a singular nonlinearity

Abdelaaziz Sbai·Youssef El hadfi
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Abstract

In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems for an elliptic equation defined by a degenerate coercive operator and a singular right hand side. \begin{equation}\label{01} \left\{ \begin{array}{lll} -\displaystyle\mbox{div}( a(x,u,\nabla u))&=\displaystyle\frac{f}{u^{\gamma}} & \mbox{ in } \Omega \\ u&>0 &\mbox{ in }\Omega \\ u&=0 &\mbox{ on } \delta\Omega \end{array} \right. \end{equation} where $\Omega $ is bounded open subset of $I\!\!R^{N}(N\geq2),$ $\gamma>0$ and $ f$ is a nonnegative function that belongs to some Lebesgue space.

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Abdelaaziz Sbai, Youssef El hadfi. 2020-05-17. Degenerate elliptic problem with a singular nonlinearity. https://doi.org/10.1080/17476933.2021.2014458

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