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 & Continuous Dynamical Systems - A, 2007, 17 (4) : 713-729. doi: 10.3934/dcds.2007.17.713
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