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Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians. (English) Zbl 1136.35016
Summary: We establish general representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians. In order to treat representation formulas on general domains, we introduce notion of ideal boundary similar to the Martin boundary [R. S. Martin, Trans. Am. Math. Soc. 49, 137–172 (1941; Zbl 0025.33302)] in potential theory. We apply such representation formulas to investigate maximal solutions, in certain classes of functions, of Hamilton-Jacobi equations.

MSC:
35F30 Boundary value problems for nonlinear first-order PDEs
35C99 Representations of solutions to partial differential equations
35F20 Nonlinear first-order PDEs
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