Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians

Hitoshi Ishii; Hiroyoshi Mitake

doi:10.1512/iumj.2007.56.3048

Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians

Hitoshi Ishii^*, Hiroyoshi Mitake

^*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

We establish general representation formulas for solutions of Hamilton-Jacobi equations widi convex Hamiltonians. In order to treat representation formulas on general domains, we introduce a notion of ideal boundary similar to the Martin boundary [21] in potential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations. Part of the results in this paper has been announced in [22]. Indiana University Mathematics Journal

Original language	English
Pages (from-to)	2159-2183
Number of pages	25
Journal	Indiana University Mathematics Journal
Volume	56
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2007.56.3048
Publication status	Published - 2007

Keywords

Aubry sets
Hamilton-Jacobi equations
Representation fotmula
State constraint problem
Weak KAM theory

ASJC Scopus subject areas

Mathematics(all)

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10.1512/iumj.2007.56.3048

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AU - Mitake, Hiroyoshi

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AB - We establish general representation formulas for solutions of Hamilton-Jacobi equations widi convex Hamiltonians. In order to treat representation formulas on general domains, we introduce a notion of ideal boundary similar to the Martin boundary [21] in potential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations. Part of the results in this paper has been announced in [22]. Indiana University Mathematics Journal

KW - Aubry sets

KW - Hamilton-Jacobi equations

KW - Representation fotmula

KW - State constraint problem

KW - Weak KAM theory

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Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians

Abstract

Keywords

ASJC Scopus subject areas

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