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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Bibliographische Detailangaben
1. Verfasser: Khavinson, Dmitry (VerfasserIn)
Körperschaft: American Mathematical Society (Herausgebendes Organ)
Weitere Verfasser: Lundberg, Erik (VerfasserIn)
Format: UnknownFormat
Sprache:eng
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2018
Schriftenreihe:Mathematical surveys and monographs volume 232
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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
Beschreibung:Includes bibliographical references and index
Beschreibung:x, 214 Seiten
Illustrationen, Diagramme
26 cm
ISBN:9781470437800
978-1-4704-3780-0