Differential and Integral Equations

Existence results for a class of degenerate elliptic equations

F. Feo, M. R. Posteraro, and G. di Blasio

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J70: Degenerate elliptic equations
Secondary: 35A01: Existence problems: global existence, local existence, non-existence 35D30: Weak solutions 35J25: Boundary value problems for second-order elliptic equations 35J62: Quasilinear elliptic equations


di Blasio, G.; Feo, F.; Posteraro, M. R. Existence results for a class of degenerate elliptic equations. Differential Integral Equations 21 (2008), no. 3-4, 387--400. https://projecteuclid.org/euclid.die/1356038786

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