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 : 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).
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 : 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).
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.
The Oblique Derivative Problem Of Potential Theory
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Author :
language : en
Publisher:
Release Date : 1998
The Oblique Derivative Problem Of Potential Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with 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 : 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 Derivative Problems For Elliptic Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 2013
Oblique Derivative Problems For Elliptic Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.
This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.
Geomathematically Oriented Potential Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2012-10-30
Geomathematically Oriented Potential Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.
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.