With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W1,p functions on bounded star domains. Our results are not obtainable from the classical inequalities for W01,p functions. Unlike in W01,p, our inequalities admit maximizers that we describe explicitly.
Hardy type inequalities radially invariant vector field Sobolev maximizers star domains trace operator
2010 MR Subject Classification
35A23 26D15 46E35
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