Classical Potential Theory
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Classical Potential Theory
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Author : David H. Armitage
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory written by David H. Armitage and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.
Brownian Motion And Classical Potential Theory
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Author : Sidney Port
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Brownian Motion And Classical Potential Theory written by Sidney Port and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
Brownian Motion and Classical Potential Theory is a six-chapter text that discusses the connection between Brownian motion and classical potential theory. The first three chapters of this book highlight the developing properties of Brownian motion with results from potential theory. The subsequent chapters are devoted to the harmonic and superharmonic functions, as well as the Dirichlet problem. These topics are followed by a discussion on the transient potential theory of Green potentials, with an emphasis on the Newtonian potentials, as well as the recurrent potential theory of logarithmic potentials. The last chapters deal with the application of Brownian motion to obtain the main theorems of classical potential theory. This book will be of value to physicists, chemists, and biologists.
Classical Potential Theory And Its Probabilistic Counterpart
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Author : Joseph L. Doob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory And Its Probabilistic Counterpart written by Joseph L. Doob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "Here is a momumental work by Doob, one of the masters, in which Part 1 develops the potential theory associated with Laplace's equation and the heat equation, and Part 2 develops those parts (martingales and Brownian motion) of stochastic process theory which are closely related to Part 1". --G.E.H. Reuter in Short Book Reviews (1985)
Classical Potential Theory
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Author : David H Armitage
language : en
Publisher:
Release Date : 2000-12-12
Classical Potential Theory written by David H Armitage and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-12 with categories.
Classical And Modern Potential Theory And Applications
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Author : K. GowriSankaran
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical And Modern Potential Theory And Applications written by K. GowriSankaran and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
Classical Potential Theory And Its Probabilistic Counterpart
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Author : J. L. Doob
language : en
Publisher: Springer
Release Date : 2012-12-05
Classical Potential Theory And Its Probabilistic Counterpart written by J. L. Doob and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-05 with Mathematics categories.
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Potential Theory
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Author : Lester Helms
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-27
Potential Theory written by Lester Helms and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-27 with Mathematics categories.
The ?rst six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. Atthetimeof the writing of that book, I had access to excellent articles,books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A n- comer to the subject will ?nd the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the Am- ican Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “. . . When I read a journal article, I often ?nd mistakes. Whether I can ?x them is irrelevant. The literature is unreliable. ” From time to time, someone must try to ?nd a path through the maze. In planning this book, it became apparent that a de?ciency in the 1969 book would have to be corrected to include a discussion of the Neumann problem, not only in preparation for a discussion of the oblique derivative boundary value problem but also to improve the basic part of the subject matter for the end users, engineers, physicists, etc.
Brownian Motion And Classical Potential Theory
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Author : Murali Rao
language : en
Publisher:
Release Date : 1977
Brownian Motion And Classical Potential Theory written by Murali Rao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Brownian motion processes categories.
Potential Theory
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Author : Lester L. Helms
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-10
Potential Theory written by Lester L. Helms and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-10 with Mathematics categories.
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
Potential Theory
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Author : John Wermer
language : en
Publisher:
Release Date : 2014-01-15
Potential Theory written by John Wermer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.