On the definition of viscosity solutions for parabolic equations

Author:
Petri Juutinen

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2907-2911

MSC (2000):
Primary 35K55, 35D99; Secondary 35B40

Published electronically:
February 15, 2001

MathSciNet review:
1840092

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Petri Juutinen**

Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40351, Jyväskylä, Finland

Email:
peanju@math.jyu.fi

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-05889-0

Keywords:
Viscosity solutions,
parabolic equations

Received by editor(s):
August 23, 1999

Received by editor(s) in revised form:
February 2, 2000

Published electronically:
February 15, 2001

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 2001
American Mathematical Society