Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains
Authors:
Nicola Garofalo and Elena Sartori
Journal:
Proc. Amer. Math. Soc. 129 (2001), 3603-3610
MSC (1991):
Primary 35K55
DOI:
https://doi.org/10.1090/S0002-9939-01-05993-7
Published electronically:
June 28, 2001
MathSciNet review:
1860493
Full-text PDF
Abstract | References | Similar Articles | Additional Information
We use the method of Alexandroff-Serrin to establish the spherical symmetry of the ground domain and of the weak solution to a free boundary problem for a class of quasi-linear parabolic equations in an unbounded cylinder , where
, with
a simply connected bounded domain. The equations considered are of the type
, with
modeled on
. We consider a solution satisfying the boundary conditions:
for
, and
,
as
. We show that the overdetermined co-normal condition
for
, with
for at least one value
, forces the spherical symmetry of the ground domain and of the solution.
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Additional Information
Nicola Garofalo
Affiliation:
Institut Mittag-Leffler, Auravägen 17, S-182 62 Djursholm, Sweden
Address at time of publication:
Department of Mathematics, The Johns Hopkins University, 3400 N. Charles St., Baltimore, Maryland 21218
Email:
garofalo@ml.kva.se
Elena Sartori
Affiliation:
Dipartimento di Metodi e Modelli Matematici, Universitá di Padova, 35131 Padova, Italy
Email:
sartori@math.unipd.it
DOI:
https://doi.org/10.1090/S0002-9939-01-05993-7
Received by editor(s):
April 18, 2000
Published electronically:
June 28, 2001
Additional Notes:
The first author was supported by NSF Grant No. DMS-9706892.
Communicated by:
David S. Tartakoff
Article copyright:
© Copyright 2001
American Mathematical Society