On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities
Boumediene Abdellaoui, Ireneo Peral · Communications on Pure & Applied Analysis · 2003
The present work is devoted to analyze the Dirichlet problem forquasilinear elliptic equation related to someCaffarelli-Kohn-Nirenberg inequalities. Precisely the problemunder study is, -div $( |x|^{-p\gamma}| ablau|^{p-2} abla 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 abounded domain in $\mathbb R^N$ such that $0\in\Omega$ and $f(x,u)$ is aCaratheodory function under suitable conditions that will bestated in each section.