Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : In this paper we improve the classical Hardy-inequality in $W^{1,p}(\Omega)$ (without boundary conditions), by showing that as in the case $p=2$, a sum of logarithmic terms can be added to the usual potential term. Moreover, in order to deal with the arbitrary boundary conditions, an integral term on some surface enclosing the origin and being contained in $\Omega$ has to be added for the inequality to hold. Finally, we show the existence of eigenvalues for a family of linear operators related to the improved Hardy inequalities above.
 
 
AN IMPROVED HARDY-SOBOLEV INEQUALITY IN W1,p AND ITS APPLICATION TO SCHRODINGER OPERATO
ADIMURTHI Adi, ESTEBAN Maria J.
2002-6
25-03-2002
 
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