Some infinite free boundary problems

Authors:
David E. Tepper and Gerald Wildenberg

Journal:
Trans. Amer. Math. Soc. **248** (1979), 135-144

MSC:
Primary 31A25

MathSciNet review:
521697

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Abstract: Let be the boundary of an unbounded simply connected region , and let denote the family of all simply connected regions such that where contains only the infinite point. For we call the free boundary of . Given a positive constant , we seek to find a region with free boundary such that there is a bounded harmonic function *V* in with the properties that (i) on , (ii) on , (iii) for . We give sufficient conditions for existence and uniqueness of . We also give quantitative properties of .

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0521697-5

Keywords:
Harmonic function,
Dirichlet problem,
free boundary

Article copyright:
© Copyright 1979
American Mathematical Society