Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : In this paper we improve the classical Hardyinequality 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. 





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