Adjoint and compensated compactness methods for Hamilton-Jacobi PDE

Abstract

We investigate the vanishing viscosity limit for Hamilton-Jacobi PDE with nonconvex Hamiltonians, and present a new method to augment the standard viscosity solution approach. The main idea is to introduce a solution σε of the adjoint of the formal linearization, and then to integrate by parts with respect to the density σε. This procedure leads to a natural phase space kinetic formulation and also to a new compensated compactness technique. © 2010 The Author(s).