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Author: Naum S. Landkof Publisher: Springer ISBN: 9783642651830 Category : Mathematics Languages : en Pages : 0
Book Description
For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation of the mathematical apparatus of potentials of single and double layers; this was adequate for treating problems involving smooth boundaries. A. M. Lyapunov is to be credited with the rigorous analysis of the properties of potentials and the possibilities for applying them to the 1 solution of boundary-value problems. The results he obtained at the end of the 19th century later received a more detailed and sharpened exposition in the book by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.
Author: Naum S. Landkof Publisher: Springer ISBN: 9783642651830 Category : Mathematics Languages : en Pages : 0
Book Description
For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation of the mathematical apparatus of potentials of single and double layers; this was adequate for treating problems involving smooth boundaries. A. M. Lyapunov is to be credited with the rigorous analysis of the properties of potentials and the possibilities for applying them to the 1 solution of boundary-value problems. The results he obtained at the end of the 19th century later received a more detailed and sharpened exposition in the book by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.
Author: Oliver Dimon Kellogg Publisher: Springer Science & Business Media ISBN: 3642908500 Category : Mathematics Languages : en Pages : 392
Book Description
The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, in order that the book may present sound ideals to the student, and also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Author: Kellogg Oliver Dimon Publisher: Barman Press ISBN: 1406706485 Category : Philosophy Languages : en Pages : 396
Book Description
Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
Author: Friedrich Schiller Publisher: Megali Verlag ISBN: 9783387053944 Category : Fiction Languages : de Pages : 0
Book Description
Reproduktion des Originals. Der Verlag Megali spezialisiert sich auf die Reproduktion historischer Werke in Großdruck, um Menschen mit eingeschränkter Sehfähigkeit das Lesen zu erleichtern.
Author: Oliver Dimon Kellogg Publisher: Courier Corporation ISBN: 9780486601441 Category : Science Languages : en Pages : 404
Book Description
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Author: Olav Kallenberg Publisher: Springer Nature ISBN: 3030618714 Category : Mathematics Languages : en Pages : 946
Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author: Naum S. Landkof
Author: Naum S. Landkof
Author: Naum S. Landkof
Author: N. S. Landkof
Author: Oliver Dimon Kellogg
Author: Kellogg Oliver Dimon
Author: Oliver D. Kellogg
Author: Friedrich Schiller
Author: Oliver Dimon Kellogg
Author: Olav Kallenberg
Author: Naum Samojlovič Landkof