A uniqueness theorem for a free boundary problem

Dancer, E.; Du, Yihong

doi:10.1090/S0002-9939-06-08409-7

A uniqueness theorem for a free boundary problem
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by E. N. Dancer and Yihong Du PDF

Proc. Amer. Math. Soc. 134 (2006), 3223-3230 Request permission

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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