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Zbl 0937.32007
Gustafsson, Björn; Putinar, Mihai
An exponential transform and regularity of free boundaries in two dimensions. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 26, No.3, 507-543 (1998). ISSN 0391-173X

The authors investigate important analytic continuation properties of the so-called exponential transform $E(z,w)$ of two complex variables. It contains an exponential function of the Cauchy integral of the characteristic function of the domain of integration. The main result is proved, which states that the Cauchy transform provides an analytic continuation for the exponential transform from $C\Omega$ through the boundary $\delta\Omega$ in both variables.\par The results are applied to the reqularity theory for free boundaries in two dimensions.
[Semen B.Yakubovich (Eindhoven)]

MSC 2000:: *32D15 Continuation of analytic objects (several variables)
30E20 Integration (one complex variable)
35R35 Free boundary problems for PDE

Keywords: free boundary; analytic continuation; Cauchy integral

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