Skip to main content

Foundations of Potential Theory

  • Book
  • © 1967

Overview

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 31)

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 9.99 USD 39.99
Discount applied Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

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, that the book may present sound ideals to the student, and in order 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.

Similar content being viewed by others

Keywords

Table of contents (12 chapters)

Authors and Affiliations

  • Harvard University, Cambridge, USA

    Oliver Dimon Kellogg

Bibliographic Information

  • Book Title: Foundations of Potential Theory

  • Authors: Oliver Dimon Kellogg

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-86748-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1967

  • Softcover ISBN: 978-3-642-86750-7Published: 15 April 2012

  • eBook ISBN: 978-3-642-86748-4Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: X, 386

  • Topics: Potential Theory, Mathematical Methods in Physics

Publish with us