Ultracontractive bounds on Hamilton-Jacobi solutions |
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Authors: | Ivan Gentil |
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Institution: | Université Paul Sabatier, Laboratoire de Statistique et Probabilités, 118 route de Narbonne, 31062 Toulouse cedex 04, France |
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Abstract: | Following the equivalence between logarithmic Sobolev inequality, hypercontractivity of the heat semigroup showed by Gross and hypercontractivity of Hamilton-Jacobi equations, we prove, like the Varopoulos theorem, the equivalence between Euclidean-type Sobolev inequality and an ultracontractive control of the Hamilton-Jacobi equations. We obtain also ultracontractive estimations under general Sobolev inequality which imply in the particular case of a probability measure, transportation inequalities. |
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Keywords: | Hamilton-Jacobi equation Sobolev inequality Ultracontractivity Transportation inequality |
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