The Cauchy problem and Hadamard's example
Jan Persson (1976)
Journées équations aux dérivées partielles
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Jan Persson (1976)
Journées équations aux dérivées partielles
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H. Marcinkowska (1971)
Annales Polonici Mathematici
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G. Métivier (1993)
Inventiones mathematicae
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Mattila, Pertti (1998)
Documenta Mathematica
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Józef Siciak (1990)
Colloquium Mathematicae
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Angus E. Taylor (1937)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Antoni Augustynowicz (1999)
Annales Polonici Mathematici
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We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
Koh, E.K., Li, C.K. (1993)
International Journal of Mathematics and Mathematical Sciences
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Luigi Rodino (1985)
Publications mathématiques et informatique de Rennes
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Guy David (1999)
Publicacions Matemàtiques
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For K ⊂ C compact, we say that K has vanishing analytic capacity (or γ(K) = 0) when all bounded analytic functions on CK are constant. We would like to characterize γ(K) = 0 geometrically. Easily, γ(K) > 0 when K has Hausdorff dimension larger than 1, and γ(K) = 0 when dim(K) < 1. Thus only the case when dim(K) = 1 is interesting. So far there is no characterization of γ(K) = 0 in general, but the special case when the Hausdorff measure H(K) is finite was recently settled....
Dubinin, V.N., Èĭrikh, N.V. (2004)
Zapiski Nauchnykh Seminarov POMI
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Pertti Mattila (1996)
Publicacions Matemàtiques
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We show that if a Cantor set E as considered by Garnett in [G2] has positive Hausdorff h-measure for a non-decreasing function h satisfying ∫ r h(r) dr < ∞, then the analytic capacity of E is positive. Our tool will be the Menger three-point curvature and Melnikov’s identity relating it to the Cauchy kernel. We shall also prove some related more general results.