Adjoint and Compensated Compactness Methods for Hamilton–Jacobi PDE
- Author(s): Evans, Lawrence C.
- et al.
Published Web Locationhttps://doi.org/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 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.