The sharp constant in Hardy's inequality for complement of bounded domain

Sharp convex Lorentz–Sobolev inequalities

“…Note that the following Hardy inequality in R n holds for 1 < p < n (see [19,34,51]), Since these equations hold for all origin-symmetric convex bodies L, (18) implies the statements of the lemma.…”

Hardy inequalities forp-Laplacians with Robin boundary conditions

“…µ p (B (iii). Hardy's inequality for complements of bounded domains with Dirichlet boundary conditions were for the first time studied in [MS2].…”

Hardy-type inequalities related to degenerate elliptic differential operators

“…3.53) cannot be improved in this generality. Indeed if ∇ L is the usual gradient ∇, then this constant is sharp (see [42]).…”

“…A lot of efforts have been made to give explicit values of the constant c, and even more, to find its best value c n, p (see e.g. [5,10,23,24,31,40,41,42]).…”