2017/01/04 by Jianliang Qian, Qian, Jianliang, Hung V. Tran +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Numerical Analysis (math.NA) #Probability (math.PR) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1701.01065
openalex publication_date 2017/01/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
This paper is the first attempt to systematically study properties of the effective Hamiltonian H arising in the periodic homogenization of some coercive but nonconvex Hamilton-Jacobi equations. Firstly, we introduce a new and robust decomposition method to obtain min-max formulas for a class of nonconvex H. Secondly, we analytically and numerically investigate other related interesting phenomena, such as "quasi-convexification" and breakdown of symmetry, of H from other typical nonconvex Hamiltonians. Finally, in the appendix, we show that our new method and those a priori formulas from the periodic setting can be used to obtain stochastic homogenization for same class of nonconvex Hamilton-Jacobi equations. Some conjectures and problems are also proposed.