, Volume 197, Issue 3, pp 1053-1088,
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Date: 17 Apr 2010

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 σ ε of the adjoint of the formal linearization, and then to integrate by parts with respect to the density σ ε . This procedure leads to a natural phase space kinetic formulation and also to a new compensated compactness technique.

Communicated by C. Dafermos
L. C. Evans was supported in part by NSF Grant DMS-0500452.