Hypercontractivity of a semi-Lagrangian scheme for Hamilton-Jacobi equations
Numerical Analysis
2013-12-12 v1
Abstract
The equivalence between logarithmic Sobolev inequalities and hypercontractivity of solutions of Hamilton-Jacobi equations has been proved in [5]. We consider a semi-Lagrangian approximation scheme for the Hamilton-Jacobi equation and we prove that the solution of the discrete problem satisfies a hypercontractivity estimate. We apply this property to obtain an error estimate of the set where the truncation error is concentrated.
Keywords
Cite
@article{arxiv.1312.3151,
title = {Hypercontractivity of a semi-Lagrangian scheme for Hamilton-Jacobi equations},
author = {Fabio Camilli and Paola Loreti and Cristina Pocci},
journal= {arXiv preprint arXiv:1312.3151},
year = {2013}
}