A Fatou theorem for the equation

Author:
Marianne K. Korten

Journal:
Proc. Amer. Math. Soc. **128** (2000), 439-444

MSC (1991):
Primary 35K65, 31A20

DOI:
https://doi.org/10.1090/S0002-9939-99-05386-1

Published electronically:
September 24, 1999

MathSciNet review:
1670395

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Abstract | References | Similar Articles | Additional Information

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 Stefan-type 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 Radon-Nikodym derivative of the initial trace with respect to Lebesgue measure and are the parabolic ``non-tangential" approach regions. Since only is continuous, while is usually not, does not hold in general.

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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:
https://doi.org/10.1090/S0002-9939-99-05386-1

Received by editor(s):
February 28, 1998

Published electronically:
September 24, 1999

Additional Notes:
This research was partially supported by PIDs 3668/92 and 3164/92-CONICET and EX 071-UBA

Dedicated:
Dedicated to the memory of Eugene Fabes

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 1999
American Mathematical Society