Metric Hopf-Lax formula with semicontinuous data

Federica Dragoni

doi:10.3934/dcds.2007.17.713

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2007, Volume 17, Issue 4: 713-729. Doi: 10.3934/dcds.2007.17.713

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Metric Hopf-Lax formula with semicontinuous data

Federica Dragoni^1,

1.
Scuola Normale Superiore, Piazza dei Cavalieri 7, P.O. Box 56126, Pisa

Received: February 28, 2006

Revised: July 31, 2006

Published: September 2007

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Abstract

In this paper we study a metric Hopf-Lax formula looking in particular at the Carnot-Carathéodory case. We generalize many properties of the classical euclidean Hopf-Lax formula and we use it in order to get existence results for Hamilton-Jacobi-Cauchy problems satisfying a suitable Hörmander condition.

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Mathematics Subject Classification: Primary: 35F25, 49L20; Secondary: 49L25, 53C17.

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