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