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Transactions of the American Mathematical Society

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Applications of variational inequalities to the existence theorem on quadrature domains


Author: Makoto Sakai
Journal: Trans. Amer. Math. Soc. 276 (1983), 267-279
MSC: Primary 31A05; Secondary 31B05, 49A29
MathSciNet review: 684507
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Abstract: In this paper we shall study quadrature domains for the class of subharmonic functions. By using the theory of variational inequalities, we shall give a new proof of the existence and uniqueness theorem. As an application, we deal with Hele-Shaw flows with a free boundary and show that their two weak solutions, one of which was defined by the author using quadrature domains and the other was defined by Gustafsson [3] using variational inequalities, are identical with each other.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0684507-2
Keywords: Quadrature domains, variational inequalities, subharmonic functions, potentials
Article copyright: © Copyright 1983 American Mathematical Society