On the definition of viscosity solutions for parabolic equations

Juutinen, Petri

doi:10.1090/S0002-9939-01-05889-0

On the definition of viscosity solutions for parabolic equations
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Proc. Amer. Math. Soc. 129 (2001), 2907-2911 Request permission

Abstract:

In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.

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