Hypercontractivity, Hopf-Lax type formulas, Ornstein-Uhlenbeck operators (II)

Antonio Avantaggiati; Paola Loreti

doi:10.3934/dcdss.2009.2.525

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2009, Volume 2, Issue 3: 525-545. Doi: 10.3934/dcdss.2009.2.525

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Hypercontractivity, Hopf-Lax type formulas, Ornstein-Uhlenbeck operators (II)

Antonio Avantaggiati^1, and
Paola Loreti^2,

1.
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Università di Roma, via A. Scarpa 16, 00161 Roma
2.
Dipartimento Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza", Via A. Scarpa, 16, 00161 Roma

Received: September 30, 2008

Revised: February 28, 2009

Published: August 2009

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Abstract

In this paper we study Hopf-Lax formulas, hypercontractivity, ultracontractivity, logarithmic Sobolev inequalities for a class of first order Hamilton-Jacobi equations.

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Mathematics Subject Classification: Primary: 35F25,49L25; Secondary: 26D15.

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