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June  2007, 6(2): 411-428. doi: 10.3934/cpaa.2007.6.411

Hardy type inequalities and Gaussian measure

Barbara Brandolini 1, , Francesco Chiacchio 1, and  Cristina Trombetti 1,

1. 

Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli, Italy, Italy, Italy

Received  June 2006 Revised  January 2007 Published  March 2007

In this paper we prove some improved Hardy type inequalities with respect to the Gaussian measure. We show that they are strictly related to the well-known Gross Logarithmic Sobolev inequality. Some applications to elliptic P.D.E.'s are also given.
Keywords: degenerate elliptic P.D.E.'s., Gaussian symmetrization, Hardy type inequalities.
Mathematics Subject Classification: Primary: 46E30, 35J70; Secondary: 35J3.
Citation: Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti. Hardy type inequalities and Gaussian measure. Communications on Pure & Applied Analysis, 2007, 6 (2) : 411-428. doi: 10.3934/cpaa.2007.6.411
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