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Summary: Preprint di Matematica - n. 1 Gennaio 2006
Metric Hopf-Lax Formula with
Semicontinuous Data
Federica Dragoni
SCUOLA NORMALE SUPERIORE
PISA
Metric Hopf-Lax Formula with
Semicontinuous Data.
Federica Dragoni.
Abstract
In this paper we study a metric Hopf-Lax formula looking in parti-
cular at the Carnot-Carath´eodory case. We generalize many proper-
ties of the classical euclidean Hopf-Lax formula and we use it in order
to get existence results for Hamilton-Jacobi-Cauchy problems satisfy-
ing a suitable H¨ormander condition.
Contents
1 Introduction. 1
2 Generalized distances and the metric Hopf-Lax function. 2
3 The generalized eikonal equation. 10
4 Hopf-Lax solution for the Cauchy problem. 16
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