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| A Representation Formula of the Viscosity Solution of the Contact Hamilton-Jacobi Equation and Its Applications |
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Citation： |
Panrui NI,Lin WANG,Jun YAN.A Representation Formula of the Viscosity Solution of the Contact Hamilton-Jacobi Equation and Its Applications[J].Chinese Annals of Mathematics B,2025,46(3):449~480 |
| Page view： 115
Net amount： 46 |
Authors： |
Panrui NI; Lin WANG;Jun YAN |
Foundation： |
the National Natural Science Foundation of China (Nos. 12122109,11790272). |
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| Abstract： |
where $H(x,u,p)$ is continuous, convex and coercive in $p$,
uniformly Lipschitz in $u$. By introducing a solution semigroup, the
authors provide a representation formula of the viscosity solution
of the evolutionary equation. As its applications, they obtain a
necessary and sufficient condition for the existence of the
viscosity solutions of the stationary equations. Moreover, they
prove a new comparison theorem depending on the neighborhood of the
projected Aubry set essentially, which is different from the one
for the Hamilton-Jacobi equation independent of $u$. |
Keywords： |
Weak KAM theory Hamilton-Jacobi equations Aubry sets |
Classification： |
37J51, 35F21, 35D40 |
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