Function theoretic methods in partial differential equations / Robert P. Gilbert.

Format:

Book

Author/Creator:

Gilbert, Robert P., 1932-

Series:

Mathematics in science and engineering ; v. 54.

Mathematics in science and engineering ; v. 54

Language:

English

Subjects (All):

Differential equations, Partial.

Functions of complex variables.

Physical Description:

1 online resource (335 p.)

Place of Publication:

New York : Academic Press, 1969.

Language Note:

English

Summary:

Function theoretic methods in partial differential equations

Contents:

Front Cover; Function Theoretic Methods in Partial Differential Equations; Copyright Page; Contents; Preface; Introduction; Chapter 1. An introduction to the theory of several complex variables; 1. Fundamentals of the Local Theory; 2. Hartogs' Theorem and Holomorphic Continuation; 3. Singular Points of Holomorphic Functions; 4. Elementary Bounds for Holomorphic Functions; References and Additional Reading; Chapter 2. Harmonic functions in (p + 2) variables; Introduction; 1. Harmonic Functions of Three Variables; 2. The Bergman-Whittaker Operator

3. Location of Singularities of Harmonic Functions4. Other Operators Generating Harmonic Functions in Three Variables; 5. Harmonic Functions in Four Variables; 6. Harmonic Functions in N >= 5 Variables; 7. The Elliptic Operator Tp+2; References and Additional Reading; Chapter 3. Elliptic differential equations in two variables with analytic coefficients; Introduction; 1. Bergman's Integral Operator of the First Kind; 2. Analytic Computations of the Bergman E-Function; 3. Fundamental Solutions, Initial Value, and Boundary Value Problems; 4. The Complex Riemann Function: Vekua's Approach

5. Existence Theorems for Nonlinear EquationsReferences and Additional Reading; Chapter 4. Singular partial differential equations; 1. Integral Operators for Axially Symmetric Potentials; 2. Analytic Properties of Generalized Axially Symmetric Potentials; 3. GASPT Functions with Entire and Meromorphic Associates; 4. Generalized Axially Symmetric Elliptic Partial Differential Equations in Normal Form; 5. The Generalized Biaxially Symmetric Helmholtz Equation (GBSHE); 6. The Generalized Biaxially Symmetric Schrödinger Equation (GBSSE)

7. The Generalized Axially Symmetric Helmholtz Equation in (N + 1) Variables (GASHN)8. Weinstein's Theory of Singular Differential Equations; References and Additional Reading; Chapter 5. Applications of integral operators to scattering problems; 1. Potential Scattering in Quantum Mechanics; 2. A Generalized Potential Scattering Problem; 3. Single Channel Scattering of Particles with Spin; 4. Inelastic Scattering and Multichannel Theory; 5. Relativistic Scattering; 6. The Inverse Scattering Problem; References and Additional Reading; References; Subject Index

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

1-282-28937-3

9786612289378

0-08-095562-2

OCLC:

316566896