On the definition of viscosity solutions for parabolic equations

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RESEARCH PRODUCT

On the definition of viscosity solutions for parabolic equations

subject

Moment (mathematics)Applied Mathematics General Mathematics Viscosity (programming)Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Test functions for optimization Calculus Parabolic partial differential equation Mathematics

description

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.

year	journal	country	edition	language
2001-02-15	Proceedings of the American Mathematical Society

https://doi.org/10.1090/s0002-9939-01-05889-0

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