Sharp Hardy inequalities on the solid torus

Abstract

In this paper, we establish the classical Hardy inequality in the solid torus and some variants of it. The general idea is to use the fact that Sobolev embeddings can be improved in the presence of symmetries. In all cases, using techniques that exploit the symmetry presented by the solid torus, we calculate the displayed best constants and we prove that they are the same as the standard Hardy best constants which appear in convex domains although the solid torus is not convex.