Archive for Rational Mechanics and Analysis

, Volume 197, Issue 3, pp 1053–1088

Adjoint and Compensated Compactness Methods for Hamilton–Jacobi PDE

Open AccessArticle

DOI: 10.1007/s00205-010-0307-9

Cite this article as:
Evans, L.C. Arch Rational Mech Anal (2010) 197: 1053. doi:10.1007/s00205-010-0307-9


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.

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© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA