Metric Hopf-Lax formula with semicontinuous data
Federica Dragoni
Discrete & Continuous Dynamical Systems - A 2007, 17(4): 713-729 doi: 10.3934/dcds.2007.17.713
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.
keywords: Hopf-Lax formula Hamilton-Jacobi equations Carnot-Carathéodory distances. Dynamical Programming Principle
Evolution by mean curvature flow in sub-Riemannian geometries: A stochastic approach
Nicolas Dirr Federica Dragoni Max von Renesse
Communications on Pure & Applied Analysis 2010, 9(2): 307-326 doi: 10.3934/cpaa.2010.9.307
We study evolution by horizontal mean curvature flow in sub- Riemannian geometries by using stochastic approach to prove the existence of a generalized evolution in these spaces. In particular we show that the value function of suitable family of stochastic control problems solves in the viscosity sense the level set equation for the evolution by horizontal mean curvature flow.
keywords: stochastic processes and control. level set equation sub-Riemannian geometries Mean curvature flow

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