TY - JOUR
T1 - Representation formulas for solutions of Hamilton-Jacobi equations with convex hamiltonians
AU - Ishii, Hitoshi
AU - Mitake, Hiroyoshi
PY - 2007
Y1 - 2007
N2 - 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
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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U2 - 10.1512/iumj.2007.56.3048
DO - 10.1512/iumj.2007.56.3048
M3 - Article
AN - SCOPUS:39049118711
SN - 0022-2518
VL - 56
SP - 2159
EP - 2183
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 5
ER -