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

 

A uniqueness theorem for a free boundary problem


Authors: E. N. Dancer and Yihong Du
Journal: Proc. Amer. Math. Soc. 134 (2006), 3223-3230
MSC (2000): Primary 35J25, 35J85, 49J40
Published electronically: May 11, 2006
MathSciNet review: 2231905
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Abstract: In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.


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Additional Information

E. N. Dancer
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Email: normd@maths.usyd.edu.au

Yihong Du
Affiliation: School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351, Australia
Email: ydu@turing.une.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08409-7
PII: S 0002-9939(06)08409-7
Keywords: Free boundary problem, variational inequality, elliptic equation
Received by editor(s): April 30, 2003
Received by editor(s) in revised form: May 15, 2005
Published electronically: May 11, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.