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Hypercontractivity of a semi-Lagrangian scheme for Hamilton-Jacobi equations

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.

preprint2013arXivOpen access
Fabio CamilliPaola LoretiCristina Pocci
math.NA
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Fabio CamilliPaola LoretiCristina Pocci

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