The Effect of Curvature on the Best Constatnt in the Hardy-Sobolev Inequalities

N. Ghoussoub, F. Robert

We address the question of attainability of the best constant in the following Hardy-Sobolev inequality on a smooth domain $\Omega$ of \mathbb{R}^n: $$ μ_s (Ω) := \inf \{\int_Ω| \nabla…