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Hopf-Lax type formulas and hypercontractivity

机译:Hopf-Lax type formulas and hypercontractivity

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摘要

Here we study where Han even, non negative, convex function, positively homogeneous of degree q as solution, in the viscosity sense, of an appropriate Hamilton—Jacobi equation.We show hypercontractivity and ultracontractivity inequalities, Logarithmic SobolevInequalities, Entropy-Energy inequality, and the optimality of the inequalities.

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