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Some Improperly Posed Problems of Mathematical Physics

  • M. M. Lavrentiev

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 11)

Table of contents

  1. Front Matter
    Pages i-vii
  2. M. M. Lavrentiev
    Pages 13-44
  3. M. M. Lavrentiev
    Pages 45-69
  4. Back Matter
    Pages 70-75

About this book

Introduction

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 . . . . . . .

Keywords

Mathematische Physik Potential equation function mathematical physics variable

Authors and affiliations

  • M. M. Lavrentiev
    • 1
  1. 1.Siberian DepartmentAcademy of ScienceNovosibirskU.d.S.S.R.

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-88210-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1967
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88212-8
  • Online ISBN 978-3-642-88210-4
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site