Abstract:

To the weighed Sobolev-Hardy inequality containing a positive constant C‚the main obstacle is that the method used to the case β＝0does not works anywhere when β≠0．That is to say‚when β＝0‚the method of Schwarz symmetrization can be employed‚but there is no reason to believe that the Schwarz symmetrization still diminishes the weighed L p -gradient or increases the weighed L p∗-norm of a function．So another approach must be found to the Sobolev-Hardy inequality．In this paper‚by Bliss lemma‚it is proved that there exists a best constant C such that the weighed Sobolev-Hardy inequality is right．

Key words: p-Laplace equation, critical exponent, best constant, Sobolev-Hardy inequality