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Linear holomorphic partial differential equations and classical potential theory

Author: Dmitry Khavinson; Erik Lundberg
Publisher: Providence, Rhode Island : American Mathematical Society, [2018]
Series: Mathematical surveys and monographs, volume 232.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Khavinson, Dmitry.
Linear holomorphic partial differential equations and classical potential theory.
Providence, Rhode Island : American Mathematical Society, [2018]
(DLC) 2017055519
(OCoLC)1019837102
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dmitry Khavinson; Erik Lundberg
ISBN: 9781470447663 1470447665
OCLC Number: 1047784385
Description: 1 online resource
Contents: 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.
Series Title: Mathematical surveys and monographs, volume 232.
Responsibility: Dmitry Khavinson, Erik Lundberg.

Abstract:

Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in  Read more...

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