The effects of a discontinues weight for a problem with a critical nonlinearity

Rejeb Hadiji, Sami Baraket, Yabib Yazidi

We study the minimizing problem $\inf \left\{{\int }_{\Omega }p(x)|\nabla u{|}^{2}dx,u\in H_0^1(\Omega ),\Vert u{\Vert }_{L^{\frac{2N}{N-2}}(\Omega )}=1\right\}$ where $\Omega$ is a smooth bounded dom…