The Oblique Derivative Problem Of Potential Theory
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The Oblique Derivative Problem Of Potential Theory
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Author : A.T. Yanushauakas
language : en
Publisher: Springer
Release Date : 2013-05-14
The Oblique Derivative Problem Of Potential Theory written by A.T. Yanushauakas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-14 with Mathematics categories.
An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to the study of singular integral equa tions, where the Fredholm alternative is violated for these problems. Thanks to de velopments in the theory of one-dimensional singular integral equations [28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at the present time [13, 29], which cannot be said about bound ary problems for elliptic equations with many independent variables. A number of important questions in this area have not yet been solved, since one does not have sufficiently general methods for investigating them. Among the boundary problems of great interest is the oblique derivative problem for harmonic functions, which can be formulated as follows: In a domain D with sufficiently smooth boundary r find a harmonic function u(X) which, on r, satisfies the condition n n ~ au ~ . . . :;. . ai (X) ax. = f (X), . . . :;. . [ai (X)]2 = 1, i=l t i=l where aI, . . . , an,fare sufficiently smooth functions defined on r. Obviously the left side of the boundary condition is the derivative of the function u(X) in the direction of the vector P(X) with components al (X), . . . , an(X).
The Oblique Derivative Problem Of Potential Theory
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Author : Alʹgimantas Ionosovich I͡Anushauskas
language : en
Publisher: Springer
Release Date : 1989-04-30
The Oblique Derivative Problem Of Potential Theory written by Alʹgimantas Ionosovich I͡Anushauskas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-04-30 with Mathematics categories.
An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to the study of singular integral equa tions, where the Fredholm alternative is violated for these problems. Thanks to de velopments in the theory of one-dimensional singular integral equations [28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at the present time [13, 29], which cannot be said about bound ary problems for elliptic equations with many independent variables. A number of important questions in this area have not yet been solved, since one does not have sufficiently general methods for investigating them. Among the boundary problems of great interest is the oblique derivative problem for harmonic functions, which can be formulated as follows: In a domain D with sufficiently smooth boundary r find a harmonic function u(X) which, on r, satisfies the condition n n ~ au ~ . . . :;. . ai (X) ax. = f (X), . . . :;. . [ai (X)]2 = 1, i=l t i=l where aI, . . . , an,fare sufficiently smooth functions defined on r. Obviously the left side of the boundary condition is the derivative of the function u(X) in the direction of the vector P(X) with components al (X), . . . , an(X).
The Oblique Derivative Problem Of Potential Theory
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Author : A.T. Yanushauakas
language : en
Publisher: Springer
Release Date : 2012-04-06
The Oblique Derivative Problem Of Potential Theory written by A.T. Yanushauakas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-06 with Mathematics categories.
An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob lems, whose investigation reduces, as a rule, to the study of singular integral equa tions, where the Fredholm alternative is violated for these problems. Thanks to de velopments in the theory of one-dimensional singular integral equations [28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at the present time [13, 29], which cannot be said about bound ary problems for elliptic equations with many independent variables. A number of important questions in this area have not yet been solved, since one does not have sufficiently general methods for investigating them. Among the boundary problems of great interest is the oblique derivative problem for harmonic functions, which can be formulated as follows: In a domain D with sufficiently smooth boundary r find a harmonic function u(X) which, on r, satisfies the condition n n ~ au ~ . . . :;. . ai (X) ax. = f (X), . . . :;. . [ai (X)]2 = 1, i=l t i=l where aI, . . . , an,fare sufficiently smooth functions defined on r. Obviously the left side of the boundary condition is the derivative of the function u(X) in the direction of the vector P(X) with components al (X), . . . , an(X).
An Alternative Approach To The Oblique Derivative Problem In Potential Theory
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Author : Frank Bauer
language : en
Publisher:
Release Date : 2004
An Alternative Approach To The Oblique Derivative Problem In Potential Theory written by Frank Bauer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
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.
Oblique Boundary Value Problems And Limit Formulae Of Potential Theory
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Author : Thomas Raskop
language : en
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2010-01
Oblique Boundary Value Problems And Limit Formulae Of Potential Theory written by Thomas Raskop and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01 with categories.
This book deals with two main subjects which are of interest in the field of geomathematics. Here we search for harmonic functions satisfying certain boundary conditions. Often this is a condition on the derivative in direction of the gravity vector. Thus an oblique boundary problem occurs, because the gravity vector is not the normal vector of the earths surface. In this book we provide weak solutions to oblique boundary problems for very general coefficients, surfaces and inhomogeneities. We start with the problem for bounded domains solving a weak formulation for inhomogeneities in Sobolev spaces. Going to unbounded domains, we use the Kelvin transformation to get a corresponding bounded problem. Moreover Stochastic inhomogeneities, a Ritz Galerkin approximation and some examples are provided. The limit formulae are strongly related to boundary problems of potential theory, because they can be used to construct harmonic functions. We prove the formulae in several norms. The achievement is the convergence in Sobolev norms, which we use in order to prove the density of several geomathematical function systems in Sobolev spaces, e.g. the spherical harmonics.
Potential Theory And Its Applications To Basic Problems Of Mathematical Physics
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Author : Nikolaĭ Maksimovich Gi︠u︡nter
language : en
Publisher: Burns & Oates
Release Date : 1968
Potential Theory And Its Applications To Basic Problems Of Mathematical Physics written by Nikolaĭ Maksimovich Gi︠u︡nter and has been published by Burns & Oates this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Foundations Of Potential Theory
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Author : Oliver Dimon Kellogg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Foundations Of Potential Theory written by Oliver Dimon Kellogg 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 2013-11-11 with Mathematics categories.
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.
The Laplace Equation
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Author : Dagmar Medková
language : en
Publisher: Springer
Release Date : 2018-03-31
The Laplace Equation written by Dagmar Medková and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-31 with Mathematics categories.
This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.
V Hotine Marussi Symposium On Mathematical Geodesy
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Author : Fernando Sansò
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
V Hotine Marussi Symposium On Mathematical Geodesy written by Fernando Sansò 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 2013-03-09 with Science categories.
Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents developments in geodesy and related sciences, including applied mathematics, among which are many new results of high intellectual value to help readers stay on top of the latest happenings in the field.