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On the definition of viscosity solutions for parabolic equations
Author(s):
Petri
Juutinen
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2907-2911.
MSC (2000):
Primary 35K55, 35D99;
Secondary 35B40
Posted:
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.
References:
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- Juutinen, P., P. Lindqvist, and J. Manfredi, On the equivalence of viscosity solutions and weak solutions for a quasilinear equation, manuscript (2000).
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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:
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
Posted:
February 15, 2001
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2001,
American Mathematical Society
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