Special Session 94: Dynamics and Variational Methods of Quasi-Hamiltonian Systems

Comparison principle of general Hamilton-Jacobi equations and applications
Gengyu Liu
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Peoples Rep of China
Co-Author(s):    Zhang Jianlu, Tu Son
Abstract:
In this talk, we investigate contact Hamilton-Jacobi equations $H(x, du, u) = c$ and $H(x, du, u) = c + \Delta u$ under the condition that the contact direction is not strictly positive definite. Correspondingly, we describe the structure of $\mathfrak{C}$ containing all the $c \in\mathbb{R}$ that makes the equations solvable and establish general comparison principles. As applications, we employ these comparison principles to obtain quantitative homogenization results.