December  2003, 2(4): 539-566. doi: 10.3934/cpaa.2003.2.539

On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities

1. 

Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain, Spain

Received  January 2003 Revised  July 2003 Published  October 2003

The present work is devoted to analyze the Dirichlet problem for quasilinear elliptic equation related to some Caffarelli-Kohn-Nirenberg inequalities. Precisely the problem under study is,

-div $( |x|^{-p\gamma}|\nabla u|^{p-2}\nabla u)=f(x, u)\in L^1(\Omega),\quad x\in \Omega$

$u(x)=0$ on $\partial \Omega,$

where $-\infty<\gamma<\frac{N-p}{p}$, $\Omega$ is a bounded domain in $\mathbb R^N$ such that $0\in\Omega$ and $f(x,u)$ is a Caratheodory function under suitable conditions that will be stated in each section.

Citation: B. Abdellaoui, I. Peral. On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities. Communications on Pure and Applied Analysis, 2003, 2 (4) : 539-566. doi: 10.3934/cpaa.2003.2.539
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