Weighted Sobolev inequalities and superlinear elliptic problems on exterior domains

Ardra A, Ameerraja Ansari, Anumol Joseph +1

Let $B_1^c=\{x\in {\mathbb{R}}^N:|x|>1\},N\ge 2$, and ${\mathcal{D}}_0^{1,N}(B_1^c)$, be the Beppo-Levi space. We prove that ${\mathcal{D}}_0^{1,N}(B_1^c)$ is compactly embedded…