# American Institute of Mathematical Sciences

October  2007, 17(4): 713-729. doi: 10.3934/dcds.2007.17.713

## Metric Hopf-Lax formula with semicontinuous data

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

Received  March 2006 Revised  August 2006 Published  January 2007

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.
Citation: Federica Dragoni. Metric Hopf-Lax formula with semicontinuous data. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 713-729. doi: 10.3934/dcds.2007.17.713
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