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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) Zbl 0546.30029

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:

30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
35A10 Cauchy-Kovalevskaya theorems
35Lxx Hyperbolic equations and hyperbolic systems
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References:

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