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Title: Linear holomorphic partial differential equations and classical potential theory (M) / Dmitry Khavinson, Erik Lundberg Dewey Class: 515.9 (DDC 23) Author: Khavinson, Dmitry, 1956- Added Personal Name: Lundberg, Erik, 1983- Publication: Providence, Rhode Island : American Mathematical Society, 2018 Physical Details: viii, 214 pages : ill.; 24 cm Series: Mathematical surveys and monographs; 232 ISBN: 9781470437800 Note: 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. ------------------------------ 0000000044010 Available at SISSA General 517.95 KHA -----------------------------------------------
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