Archive for Rational Mechanics and Analysis

, Volume 197, Issue 3, pp 1053–1088 | Cite as

Adjoint and Compensated Compactness Methods for Hamilton–Jacobi PDE

Open Access


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

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