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A uniqueness theorem for a free boundary problem. (English) Zbl 1168.35450

Summary: 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.

MSC:

35R35 Free boundary problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49J40 Variational inequalities
92D25 Population dynamics (general)
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