Some Improperly Posed Problems of Mathematical Physics (Springer Tracts in Natural Philosophy): 11 - Brossura

Lavrentiev, Michail M.

Brossura

ISBN 10: 3642882129 ISBN 13: 9783642882128

Casa editrice: Springer, 2012

Riassunto

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 . . . . . . .

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Contenuti

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..

Product Description

Book by Lavrentiev Michail M

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3642882129
• ISBN 13: 9783642882128
• Rilegatura: Copertina flessibile
• Numero di pagine: 88
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania