Some Improperly Posed Problems of Mathematical Physics

Michail M. Lavrentiev (Autor)

Buch | Softcover

VIII, 76 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1967
Springer Berlin (Verlag)
978-3-642-88212-8 (ISBN)

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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 . . . . . . .

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..

Erscheint lt. Verlag	19.4.2012
Reihe/Serie	Springer Tracts in Natural Philosophy
Überarbeitung	R.J. Sacker
Übersetzer	R.J. Sacker
Zusatzinfo	VIII, 76 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	148 g
Themenwelt	Mathematik / Informatik ► Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Equation • Function • Mathematical Physics • Mathematische Physik • Potential • Variable
ISBN-10	3-642-88212-9 / 3642882129
ISBN-13	978-3-642-88212-8 / 9783642882128
Zustand	Neuware