The free boundary of a semilinear elliptic equation

Authors:
Avner Friedman and Daniel Phillips

Journal:
Trans. Amer. Math. Soc. **282** (1984), 153-182

MSC:
Primary 35J65; Secondary 35J85, 35R35

DOI:
https://doi.org/10.1090/S0002-9947-1984-0728708-4

MathSciNet review:
728708

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Abstract | References | Similar Articles | Additional Information

Abstract: The Dirichlet problem in a domain on is considered with if if if is not monotone in general. The set and the ``free boundary'' are studied. Sharp asymptotic estimates are established as . For suitable , under the assumption that is a two-dimensional convex domain, it is shown that is a convex set. Analogous results are established also in the case where on .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0728708-4

Keywords:
Semilinear elliptic equation,
free boundary,
variational inequality,
maximal and minimal solutions,
minimizer,
asymptotic behavior,
reduced boundary,
nonnegative mean curvature

Article copyright:
© Copyright 1984
American Mathematical Society