Weak KAM theory for HAMILTON-JACOBI equations depending on unknown functions
Weak KAM theory for HAMILTON-JACOBI equations depending on unknown functions
We consider the evolutionary Hamilton-Jacobi equation depending on the unknown function with the continuous initial condition on a connected closed manifold.Under certain assumptions on $H(x,u,p)$ with respect to $u$ and $p$, we provide an implicit variational principle. By introducing an implicitly defined solution semigroup and an admissible value set $\mathcal{C}_H$, …