A Fatou theorem for the equation
Author:
Marianne K. Korten
Journal:
Proc. Amer. Math. Soc. 128 (2000), 439444
MSC (1991):
Primary 35K65, 31A20
Published electronically:
September 24, 1999
MathSciNet review:
1670395
Fulltext PDF Free Access
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Abstract: In one space dimension and for a given function (say such that in some interval), the equation can be thought of as describing the energy per unit volume in a Stefantype problem where the latent heat of the phase change is given by . Given a solution to this equation, we prove that for a.e. , there exists where is the RadonNikodym derivative of the initial trace with respect to Lebesgue measure and are the parabolic ``nontangential" approach regions. Since only is continuous, while is usually not, does not hold in general.
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P. Calderón, On the behaviour of harmonic functions
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 J. E. Bouillet, Signed solutions to diffusionheat conduction equations, Free Boundary Problems: Theory and Applications, Proc. Int. Colloq. Irsee/Ger. 1987, Vol. II, Pitman Res. Notes Math. Ser. 186 (1990), 480485.
 [BKM]
 J. E. Bouillet, M. K. Korten and V. Márquez, Singular limits and the ``Mesa" problem, Rev. Union Mat. Argentina, Vol. 41 (1998), no. 1, 2740.
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Additional Information
Marianne K. Korten
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. No. 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina;
Instituto Argentino de Matemática (CONICET), Saavedra 15, 3er. piso, 1083 Buenos Aires, Argentina
Address at time of publication:
Department of Mathematics, University of Liousville, Louisville, Kentucky 40292
Email:
mkorten@dm.uba.ar, korten@louisville.edu
DOI:
http://dx.doi.org/10.1090/S0002993999053861
PII:
S 00029939(99)053861
Received by editor(s):
February 28, 1998
Published electronically:
September 24, 1999
Additional Notes:
This research was partially supported by PIDs 3668/92 and 3164/92CONICET and EX 071UBA
Dedicated:
Dedicated to the memory of Eugene Fabes
Communicated by:
Christopher D. Sogge
Article copyright:
© Copyright 1999
American Mathematical Society
