On nonlinear elliptic equations with singular lower order term
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We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like $$\left\{ \begin{aligned} &-{\rm div}\Big((a(x)+|u|^q) \nabla u\Big)= \frac{f}{|u|^\gamma}\ \ {\rm in}\ \Omega,\\ & u=0\ \ {\rm on}\ {\partial \Omega},\\ \end{aligned} \right.$$ where $\Omega$ is a bounded open subset of $\mathbb{R^N} (N \geq 2)$, $a(x)$ is a measurable nonnegative function, $q, \gamma> 0$ and the source $f$ is a nonnegative (not identicaly zero) function belonging to $L^m(\Omega)$ for some $m \geq 1$. Our results will depend on the summability of $f$ and on the values of $q, \gamma> 0$.
Abstract
We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like $$\left\{ \begin{aligned} &-{\rm div}\Big((a(x)+|u|^q) \nabla u\Big)= \frac{f}{|u|^\gamma}\ \ {\rm in}\ \Omega,\\ & u=0\ \ {\rm on}\ {\partial \Omega},\\ \end{aligned} \right.$$ where $\Omega$ is a bounded open subset of $\mathbb{R^N} (N \geq 2)$, $a(x)$ is a measurable nonnegative function, $q, \gamma> 0$ and the source $f$ is a nonnegative (not identicaly zero) function belonging to $L^m(\Omega)$ for some $m \geq 1$. Our results will depend on the summability of $f$ and on the values of $q, \gamma> 0$.
참고문헌 (18)
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