Variational and viscosity operators for the evolutive Hamilton-Jacobi equation

Autor:	Roos, Valentine
Rok vydání:	2018
Předmět:	Mathematics - Symplectic Geometry Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax-Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable. Comment: Communications in Contemporary Mathematics, World Scientific Publishing, A Para{\^i}tre
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1801.09889 Zobrazit plný text záznamu View this record from Arxiv