## Differential and Integral Equations

### Existence results for a class of degenerate elliptic equations

#### Abstract

In the present paper we prove existence results for a class of nonlinear elliptic equations whose prototype is: $$- {\rm div} \left( \left\vert { \nabla u} \right\vert ^{{ p-2}}{ \nabla u\varphi (x)}\right) { +b(x)}\left\vert { \nabla u}\right\vert ^{ { \sigma }}{ \varphi (x)=g\varphi ,}$$ where $\Omega$ is an open set, $u=0$ on $\partial \Omega ,$ where the function $\varphi (x)=(2\pi )^{-\frac{n}{2}}$ $\exp \left( -\left\vert x\right\vert ^{2}/2\right)$ is the density of Gauss measure and $g \! \in \! L^{r}(\log L)^{-\frac{1}{2}}(\varphi ,\Omega )$ for $1 < r < p^{\prime }.$

#### Article information

Source
Differential Integral Equations, Volume 21, Number 3-4 (2008), 387-400.

Dates
First available in Project Euclid: 20 December 2012