Linear holomorphic partial differential equations and classical potential theory
Introduction: some motivating questions -- The Cauchy-Kovalevskaya theorem with estimates -- Remarks on the Cauchy-Kovalevskaya theorem -- Zerner's theorem -- The method of globalizing families -- Holmgren's uniqueness -- The continuity method of F. John -- The Bony-Schapira theorem -- App...
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Sprache: | eng |
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Providence, Rhode Island
American Mathematical Society
2018
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Schriftenreihe: | Mathematical surveys and monographs
volume 232 |
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Online Zugang: | Inhaltsverzeichnis Inhaltstext |
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Zusammenfassung: | Introduction: some motivating questions -- The Cauchy-Kovalevskaya theorem with estimates -- Remarks on the Cauchy-Kovalevskaya theorem -- Zerner's theorem -- The method of globalizing families -- Holmgren's uniqueness -- The continuity method of F. John -- The Bony-Schapira theorem -- Applications of the Bony-Schapira theorem -- The reflection principle -- The reflection principle (continued) -- Cauchy problems and the Schwarz potential conjecture -- The Schwarz potential conjecture for spheres -- Potential theory on ellipsoids: part I -- The mean value property -- Potential theory on ellipsoids: Part II -- There is no gravity in the cavity -- Potential theory on ellipsoids: part III -- The Dirichlet problem -- Singularities encountered by the analytic continuation of solutions to the Dirichlet problem -- An introduction to J. Leray's principle on propagation of singularities through Cn -- Global propagation of singularities in Cn -- Quadrature domains and Laplacian growth -- Other varieties of quadrature domains |
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Beschreibung: | Includes bibliographical references and index |
Beschreibung: | x, 214 Seiten Illustrationen, Diagramme 26 cm |
ISBN: | 9781470437800 978-1-4704-3780-0 |