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arXiv:1406.0793 [math.DS]AbstractReferencesReviewsResources

Semi-concave singularities and the Hamilton-Jacobi equation

Patrick Bernard

Published 2014-06-03Version 1

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.

Journal: Regular and Chaotic Dynamics 18, 6 (2013) 674-685
Categories: math.DS
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