On the Hardy-Sobolev-Maz'ya inequality and its generalizations

Abstract

The paper deals with natural generalizations of the Hardy-Sobolev-Maz'ya inequality and some related questions, such as the optimality and stability of such inequalities, the existence of minimizers of the associated variational problem, and the natural energy space associated with the given functional.

The paper has appeared in "Sobolev Spaces in Mathematics I: Sobolev Type Inequalities", ed. V. Maz'ya, International Mathematical Series 8, Springer, 2009, 281-297. Note that Example 2.7 has been revised, and accordingly the list of references has been updated.