The effects of a discontinues weight for a problem with a critical nonlinearity
We study the minimizing problem $\inf\left\{\displaystyle\int_Ωp(x)|\nabla u|^{2}dx,\,u\in H^{1}_{0}(Ω),\,\|u\|_{L^{\frac{2N}{N-2}}(Ω)}=1\right\}$ where $Ω$ is a smooth bounded domain of $\R^{N}$, $N\geq 3$ and $p$ a positive discontinuous function. We prove the existence of a minimizer under some assumptions.
math.AP↗