Hamilton-Jacobi方程整体解的不变性
Invariance of global solutions of the Hamilton-Jacobi equation
摘要：
证明了闭流形余切丛上与凸超线性Hamilton算子相关联的Hamilton Jacobi方程的整体黏性解在Hamilton算子的对称群的单位连通区下必是不变的（证明了此对称群是紧李群）.特别地，每个在哈密顿流下不变的拉格朗日截面在这个群下也不变。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
