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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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:

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
PII: S 0002-9939(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