Discontinuous “viscosity” solutions of a degenerate parabolic equation

Bertsch, Michiel; Dal Passo, Roberta; Ughi, Maura

doi:10.1090/S0002-9947-1990-0965742-6

Discontinuous “viscosity” solutions of a degenerate parabolic equation
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by Michiel Bertsch, Roberta Dal Passo and Maura Ughi PDF

Trans. Amer. Math. Soc. 320 (1990), 779-798 Request permission

Abstract:

We study a nonlinear degenerate parabolic equation of the second order. Regularizing the equation by adding some artificial viscosity, we construct a generalized solution. We show that this solution is not necessarily continuous at all points.

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