Linear holomorphic partial differential equations and classical potential theory / Dmitry Khavinson, Erik Lundberg.

Format:

Book

Author/Creator:

Khavinson, Dmitry, 1956- author.

Lundberg, Erik, 1983- author.

Series:

Mathematical surveys and monographs ; no. 232.

Mathematical surveys and monographs ; volume 232

Language:

English

Subjects (All):

Potential theory (Mathematics).

Differential equations, Linear.

Differential equations, Partial.

Holomorphic functions.

Partial differential equations--General topics--Analytic methods, singularities.

Potential theory--Higher-dimensional theory--Boundary value and inverse problems.

Several complex variables and analytic spaces--Holomorphic functions of several complex variables--Power series, series of functions.

Functions of a complex variable--Series expansions--Analytic continuation.

Algebraic geometry--Real algebraic and real analytic geometry--Real algebraic sets.

Local Subjects:

Partial differential equations--General topics--Analytic methods, singularities.

Potential theory--Higher-dimensional theory--Boundary value and inverse problems.

Several complex variables and analytic spaces--Holomorphic functions of several complex variables--Power series, series of functions.

Functions of a complex variable--Series expansions--Analytic continuation.

Algebraic geometry--Real algebraic and real analytic geometry--Real algebraic sets.

Differential equations, Linear.

Differential equations, Partial.

Holomorphic functions.

Potential theory (Mathematics).

Physical Description:

x, 214 pages : illustrations (chiefly color) ; 27 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

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.

Notes:

Includes bibliographical references (pages 203-210) and index.

ISBN:

9781470437800

1470437805

OCLC:

1019837102