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Zbl 0546.30029
Duchon, Jean; Robert, Raoul
Estimation d'opérateurs intégraux du type de Cauchy dans les échelles d'Ovsyannikov et application. (Estimate of intégral opérators of Cauchy type in Ovsyannikov scales and application).
(French)
[J] Ann. Inst. Fourier 36, No.1, 83-95 (1986). ISSN 0373-0956; ISSN 1777-5310/e

We establish estimates for the Cauchy singular integral and related potential operators in Ovsjannikov scales of analytic functions. These estimates are used to prove existence locally in time of analytic solutions for some free boundary problems in the plane.
MSC 2000:
*30E20 Integration (one complex variable)
35A10 Cauchy-Kowalewski theorems
35Lxx Hyperbolic equations and systems

Keywords: Cauchy singular integral operator; analytic free boundary; Ovsjannikov scales

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Scientific prize winners of the ICM 2010
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Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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