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Uniqueness results for quasilinear parabolic equations through viscosity solutions’ methods. (English) Zbl 1036.35001
Authors’ abstract: In this article, we are interested in uniqueness results for viscosity solutions of a general class of quasilinear, possibly degenerate, parabolic equations set in \({\mathbb R^n}\). Using classical viscosity solutions’ methods, we obtain a general comparison result for solutions with polynomial growths but with a restriction on the growth of the initial data. The main application is the uniqueness of solutions for the mean curvature equation for graphs which was only known in the class of uniformly continuous functions.

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35K65 Degenerate parabolic equations
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