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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the existence of convex classical solutions for multilayer free boundary problems with general nonlinear joining conditions
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by Andrew Acker PDF
Trans. Amer. Math. Soc. 350 (1998), 2981-3020 Request permission

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.
References
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Additional Information
  • Andrew Acker
  • Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
  • Received by editor(s): August 15, 1995
  • © Copyright 1998 American Mathematical Society
  • 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