Here we study u(x, t) := Qtu0(x)= y Rnu0(y)+α p 1-α pt→)q-1 H(y- e-α tx) 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 Sobolev Inequalities, Entropy-Energy inequality, and the optimality of the inequalities. © 2008 Università degli Studi di Napoli "Federico II".
Hopf-Lax type formulas and hypercontractivity / Antonio, A., Loreti, P.. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 57:2(2008), pp. 171-202. [10.1007/s11587-008-0036-7]
Hopf-Lax type formulas and hypercontractivity
LORETI, Paola
2008
Abstract
Here we study u(x, t) := Qtu0(x)= y Rnu0(y)+α p 1-α pt→)q-1 H(y- e-α tx) 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 Sobolev Inequalities, Entropy-Energy inequality, and the optimality of the inequalities. © 2008 Università degli Studi di Napoli "Federico II".File allegati a questo prodotto
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