Entropy penalization methods for Hamilton-Jacobi equations

Diogo A. Gomes, Enrico Valdinoci

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.

Original languageEnglish
Pages (from-to)94-152
Number of pages59
JournalAdvances in Mathematics
Volume215
Issue number1
DOIs
Publication statusPublished - 20 Oct 2007
Externally publishedYes

Fingerprint

Penalization Method
Entropy Method
Hamilton-Jacobi Equation
Evolution Equation
Linear equation
Entropy
Cole-Hopf Transformation
Fixed Point Problem
Penalization
Convert
Nonlinear Equations
Approximate Solution
Approximation
Generalization

Cite this

@article{5389f5c49a6a4c12b7a6578adbb26a9d,
title = "Entropy penalization methods for Hamilton-Jacobi equations",
abstract = "In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.",
keywords = "Fixed points, Hamilton-Jacobi equations, Mather measures, Semiconcave functions",
author = "Gomes, {Diogo A.} and Enrico Valdinoci",
year = "2007",
month = "10",
day = "20",
doi = "10.1016/j.aim.2007.04.001",
language = "English",
volume = "215",
pages = "94--152",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "1",

}

Entropy penalization methods for Hamilton-Jacobi equations. / Gomes, Diogo A.; Valdinoci, Enrico.

In: Advances in Mathematics, Vol. 215, No. 1, 20.10.2007, p. 94-152.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Entropy penalization methods for Hamilton-Jacobi equations

AU - Gomes, Diogo A.

AU - Valdinoci, Enrico

PY - 2007/10/20

Y1 - 2007/10/20

N2 - In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.

AB - In this paper we present a new entropy penalization problem and we discuss its relations with approximate solutions of Hamilton-Jacobi equations, the convergence of associated discrete schemes, as well as several applications, such as: a generalization of the Hopf-Cole transformation which converts non-linear Hamilton-Jacobi equations into linear evolution equations, the study of fixed point problems, approximation of certain linear evolution equations, and the construction of entropy penalized Mather measures.

KW - Fixed points

KW - Hamilton-Jacobi equations

KW - Mather measures

KW - Semiconcave functions

UR - http://www.scopus.com/inward/record.url?scp=34447498638&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2007.04.001

DO - 10.1016/j.aim.2007.04.001

M3 - Article

VL - 215

SP - 94

EP - 152

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 1

ER -