Hardy type inequalities with spherical derivatives

Abstract

A Hardy type inequality is presented with spherical derivatives in R n with n ! 2 in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments. Mathematics Subject Classification Primary 26D10 Á Secondary 35A23 Á 46E35 This article is part of the section ''Theory of PDEs'' edited by Eduardo Teixeira.