Entropy penalization methods for Hamilton-Jacobi equations

Diogo A. Gomes; Enrico Valdinoci

doi:10.1016/j.aim.2007.04.001

Entropy penalization methods for Hamilton-Jacobi equations

Diogo A. Gomes
, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

18 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 language	English
Pages (from-to)	94-152
Number of pages	59
Journal	Advances in Mathematics
Volume	215
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2007.04.001
Publication status	Published - 20 Oct 2007
Externally published	Yes

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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.",

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AU - Valdinoci, Enrico

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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 - https://www.scopus.com/pages/publications/34447498638

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DO - 10.1016/j.aim.2007.04.001

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VL - 215

SP - 94

EP - 152

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Entropy penalization methods for Hamilton-Jacobi equations

Abstract

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