Adjoint and Compensated Compactness Methods for Hamilton–Jacobi PDE

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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