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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-06-08409-7

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.