论文标题
退化的椭圆形问题与单数非线性
Degenerate elliptic problem with a singular nonlinearity
论文作者
论文摘要
在本文中，我们证明了某些非线性差异问题的解决方案的存在和规律性结果，用于由退化的强制操作员和单一的右手侧定义的椭圆方程。 \ begin {equination} \ label {01} \ left \ {\ begin {array} {lll} {lll} - \ displaystyle \ mbox {div}（a（a（x，x，x，x，u，\ nabla u）） ＆\ mbox {in}ω\\ u＆= 0＆\ mbox {on}ΔΩ\ end {array} \ right。 \ end {equation}其中$ω$是$ i \！\！r^{n}（n \ geq2）的开放子集，$ $ $umγ> 0 $和$ f $是属于某些Lebesgue Space的非负函数。
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^γ} & \mbox{ in } Ω\\ u&>0 &\mbox{ in }Ω\\ u&=0 &\mbox{ on } δΩ\end{array} \right. \end{equation} where $Ω$ is bounded open subset of $I\!\!R^{N}(N\geq2),$ $γ>0$ and $ f$ is a nonnegative function that belongs to some Lebesgue space.
