Degenerate elliptic problem with a singular nonlinearity. (English) Zbl 1514.35213
Summary: 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
\[
\begin{cases}
- \operatorname{div}(a(x, u, \nabla u)) = \frac{f}{u^\gamma} & \text{in } \Omega \\
u=0 & \text{on } \partial \Omega
\end{cases}
\tag{1}
\]
where \(\Omega\) is bounded open subset of \(I\!\!R^N\)\((N \geq 2)\), \(\gamma>0\) and \(f\) is a non-negative function that belongs to some Lebesgue space.
MSC:
| 35J70 | Degenerate elliptic equations |
| 35J75 | Singular elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
degenerate elliptic equation; Dirichlet problem; singular nonlinearity; existence; regularityReferences:
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