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

Hitoshi Ishii, Hiroyoshi Mitake

Research output: Contribution to journalArticle

30 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  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 . Indiana University Mathematics Journal

Original language English 2159-2183 25 Indiana University Mathematics Journal 56 5 https://doi.org/10.1512/iumj.2007.56.3048 Published - 2007

### Fingerprint

Representation Formula
Hamilton-Jacobi Equation
Martin Boundary
Maximal Solution
Potential Theory

### Keywords

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

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians. / Ishii, Hitoshi; Mitake, Hiroyoshi.

In: Indiana University Mathematics Journal, Vol. 56, No. 5, 2007, p. 2159-2183.

Research output: Contribution to journalArticle

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