Differential Equations and Nonlinear Analysis Seminar: Yifeng Yu, University of California – Irvine, High Degeneracy of Effective Hamiltonian in Two Dimensions
ZoomOne of the major open problems in homogenization of Hamilton-Jacobi equations is to under deep properties of the effective Hamiltonian. In this talk, I will present some recent progress. In particular, consider the effective Hamiltonian associated with the mechanical Hamiltonian H(p,x)=(|p|^2)/2+V(x). We can show that for generic V, the effective Hamiltonian is piecewise 1d in…