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Hypercontractivity of Hamilton–Jacobi equations

open access: yesJournal Des Mathematiques Pures Et Appliquees, 2001
Using the equivalence of logarithmic Sobolev inequalities and hypercontractivity of the associated heat semigroup proved by \textit{L. Gross} [Am. J. Math. 97(1975), 1061--1083 (1976; Zbl 0318.46049)], the authors show that logarithmic Sobolev inequalities are similarly related to hypercontractivity of the solutions of Hamilton-Jacobi equations.
Ivan Gentil
exaly   +3 more sources
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Linearization of the Hamilton–Jacobi equation

Journal of Mathematical Physics, 1986
Through a canonoid transformation the integration for the Hamilton–Jacobi equations is transformed into a two step procedure: the first being a linear problem and the second a quasilinear one. Examples are given.
Espindola, Maria L.   +2 more
openaire   +1 more source

The Hamilton—Jacobi Equation

2001
We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0.
Walter Dittrich, Martin Reuter
openaire   +1 more source

Relaxation of Hamilton-Jacobi Equations

Archive for Rational Mechanics and Analysis, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hitoshi Ishii, LORETI, Paola
openaire   +1 more source

Hamilton–Jacobi–Bellman Equations

2017
In this chapter we present recent developments in the theory of Hamilton–Jacobi–Bellman (HJB) equations as well as applications. The intention of this chapter is to exhibit novel methods and techniques introduced few years ago in order to solve long-standing questions in nonlinear optimal control theory of Ordinary Differential Equations (ODEs).
Festa, Adriano   +6 more
openaire   +3 more sources

The Hamilton–Jacobi equation

2020
Abstract This chapter discusses the motion of particles which are scattered by and fall towards the center of the dipol, the motion of a particle in the Coulomb and the constant electric fields, and a particle inside a smooth elastic ellipsoid.
Gleb L. Kotkin, Valeriy G. Serbo
openaire   +1 more source

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