# American Institute of Mathematical Sciences

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

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

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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