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 | References | Similar Articles | Additional Information

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