Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Sufficient condition for the existence of solutions of a free boundary problem

Authors: Mohammed Hayouni and Arian Novruzi
Journal: Quart. Appl. Math. 60 (2002), 425-435
MSC: Primary 35R35; Secondary 35J20
DOI: https://doi.org/10.1090/qam/1914434
MathSciNet review: MR1914434
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Abstract: In this paper we study the existence of critical points of a functional depending on $ \Omega \subset \mathbb{R}^{2}$ through its perimeter and the solution of the Dirichlet problem in $ \Omega $, under the constraint that the measure of $ \Omega $ is given. We give a sufficient condition for the existence of critical points using the implicit function theorem.

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DOI: https://doi.org/10.1090/qam/1914434
Article copyright: © Copyright 2002 American Mathematical Society

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