Author | Lavrentiev, M. M. author |
---|---|

Title | Some Improperly Posed Problems of Mathematical Physics [electronic resource] / by M. M. Lavrentiev |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1967 |

Connect to | http://dx.doi.org/10.1007/978-3-642-88210-4 |

Descript | VIII, 76 p. online resource |

SUMMARY

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 difยญ 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 ยง 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . ยง 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation ยง 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 ยง 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 ยง 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 ยง 4 Analytic Continuation of a Function of Two Real Variables 32 ยง 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 ยง 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations ยง 1 The Inverse Problem for a Newtonian Potential . . . . . .

CONTENT

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

Mathematics
Mathematical physics
Physics
Mathematics
Mathematical Physics
Mathematical Methods in Physics
Theoretical Mathematical and Computational Physics