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On the existence of convex classical solutions
for multilayer free boundary problems
with general nonlinear joining conditions


Author: Andrew Acker
Journal: Trans. Amer. Math. Soc. 350 (1998), 2981-3020
MSC (1991): Primary 35R35, 35J05, 76T05
DOI: https://doi.org/10.1090/S0002-9947-98-01943-6
MathSciNet review: 1422592
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Abstract: We prove the existence of convex classical solutions for a general multidimensional, multilayer free-boundary problem. The geometric context of this problem is a nested family of closed, convex surfaces. Except for the innermost and outermost surfaces, which are given, these surfaces are interpreted as unknown layer-interfaces, where the layers are the bounded annular domains between them. Each unknown interface is characterized by a quite general nonlinear equation, called a joining condition, which relates the first derivatives (along the interface) of the capacitary potentials in the two adjoining layers, as well as the spatial variables. A well-known special case of this problem involves several stationary, immiscible, two-dimensional flows of ideal fluid, related along their interfaces by Bernoulli's law.


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Additional Information

Andrew Acker
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033

DOI: https://doi.org/10.1090/S0002-9947-98-01943-6
Keywords: Multilayer elliptic free boundary problem, convexity, non-linear joining conditions
Received by editor(s): August 15, 1995
Article copyright: © Copyright 1998 American Mathematical Society

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