HARDY'S INEQUALITIES WITH MAXIMIZERS FOR W~(1,p) FUNCTIONS ON BOUNDED STAR DOMAINS

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W~(1,p) functions on bounded star domains. Our results are not obtainable from the classical inequalities for W_0~(1,p) functions. Unlike in W_0~(1,p),our inequalities admit maximizers that we describe explicitly.