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  using variational inequalities, are identical with each other.
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- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 276 (1983), 267-279
- MSC: Primary 31A05; Secondary 31B05, 49A29
- DOI: https://doi.org/10.1090/S0002-9947-1983-0684507-2
- MathSciNet review: 684507