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Our intention in this paper is to publicize and extend somewhat important work of Plotnikov [P] on the asymptotic limits of solutions of viscous regularizations of an nonlinear diffusion PDE with a cubic nonlinearity. Since the formal limit PDE is in general ill–posed, we expect that the limit solves instead a corresponding diffusion equation with(More)
To study fine properties of certain smooth approximations u ε to a viscosity solution u of the infinity Laplacian PDE, we introduce Green's function σ ε for the linearization. We can then integrate by parts with respect to σ ε and derive various useful integral estimates. We are in particular able to use these estimates (i) to prove the everywhere(More)