Invariance of global solutions of the Hamilton-Jacobi equation
Symplectic Geometry
2015-02-24 v1
Abstract
We show that every global viscosity solution of the Hamilton-Jacobi equation associated with a convex and superlinear Hamiltonian on the cotangent bundle of a closed manifold is necessarily invariant under the identity component of the group of symmetries of the Hamiltonian (We prove that this group is a compact Lie group). In particular, every Lagrangian section invariant under the Hamiltonian flow is also invariant under this group.
Keywords
Cite
@article{arxiv.1502.06563,
title = {Invariance of global solutions of the Hamilton-Jacobi equation},
author = {Ezequiel Maderna},
journal= {arXiv preprint arXiv:1502.06563},
year = {2015}
}