Semi-concave singularities and the Hamilton-Jacobi equation
Dynamical Systems
2014-06-04 v1
Abstract
We study the Cauchy problem for the Hamilton-Jacobi equation with a semiconcave initial condition. We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.
Cite
@article{arxiv.1406.0793,
title = {Semi-concave singularities and the Hamilton-Jacobi equation},
author = {Patrick Bernard},
journal= {arXiv preprint arXiv:1406.0793},
year = {2014}
}