
Some Improperly Posed Problems of Mathematical Physics
Michail M. Lavrentiev(Author)
Springer (Publisher)
Published on 19. April 2012
Book
Paperback/Softback
VIII, 76 pages
978-3-642-88212-8 (ISBN)
Description
This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 § 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 § 4 Analytic Continuation of a Function of Two Real Variables 32 § 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations § 1 The Inverse Problem for a Newtonian Potential . . . . . . .
More details
Series
Edition
Softcover reprint of the original 1st ed. 1967
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 76 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 6 mm
Weight
149 gr
ISBN-13
978-3-642-88212-8 (9783642882128)
DOI
10.1007/978-3-642-88210-4
Schweitzer Classification
Other editions
Additional editions

Michail M. Lavrentiev
Some Improperly Posed Problems of Mathematical Physics
Book
02/1967
1st Edition
Springer
€85.55
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Persons
Content
I Formulation of some Improperly Posed Problems of Mathematical Physics.- § 1 Improperly Posed Problems in Metric Spaces.- § 2 A Probability Approach to Improperly Posed Problems.- II Analytic Continuation.- § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity.- § 2 The Cauchy Problem for the Laplace Equation.- § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity.- § 4 Analytic Continuation of a Function of Two Real Variables.- § 5 Analytic Continuation of Harmonic Functions from a Circle.- § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry.- III Inverse Problems for Differential Equations.- § 1 The Inverse Problem for a Newtonian Potential.- § 2 A Class of Nonlinear Integral Equations.- § 3 Inverse Problems for Some Non-Newtonian Potentials.- § 4 An Inverse Problem for the Wave Equation.- § 5 On a Class of Inverse Problems for Differential Equations..