Holomorphic Partial Differential Equations And Classical Potential Theory

Author : Dmitry Khavinson,Erik Lundberg
Publisher : American Mathematical Soc.
Page : 214 pages
File Size : 41,9 Mb
Release : 2018-07-09
Category : Differential equations, Linear
ISBN : 9781470437800

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Linear Holomorphic Partial Differential Equations and Classical Potential Theory by Dmitry Khavinson,Erik Lundberg Pdf

Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.

Author : Dmitry Khavinson
Publisher : Unknown
Page : 123 pages
File Size : 42,6 Mb
Release : 1996-06-01
Category : Potential theory (Mathematics)
ISBN : 8460093239

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Holomorphic Partial Differential Equations and Classical Potential Theory by Dmitry Khavinson Pdf

Author : Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely
Publisher : Springer
Page : 276 pages
File Size : 46,8 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9783540459521

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Potential Theory, Surveys and Problems by Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely Pdf

The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.

Author : Lester Helms
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 40,6 Mb
Release : 2009-05-27
Category : Mathematics
ISBN : 9781848823198

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Potential Theory by Lester Helms Pdf

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.

Author : K. GowriSankaran,J. Bliedtner,D. Feyel,M. Goldstein,W.K. Hayman,I. Netuka
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401111386

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Classical and Modern Potential Theory and Applications by K. GowriSankaran,J. Bliedtner,D. Feyel,M. Goldstein,W.K. Hayman,I. Netuka Pdf

Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993

Author : Elias M. Stein
Publisher : Princeton University Press
Page : 83 pages
File Size : 41,6 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400871261

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Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11) by Elias M. Stein Pdf

This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field. Originally published in 1972. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : B. Fuglede,M. Goldstein,W. Haussmann,W.K. Hayman,L. Rogge
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401124362

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Approximation by Solutions of Partial Differential Equations by B. Fuglede,M. Goldstein,W. Haussmann,W.K. Hayman,L. Rogge Pdf

This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In addition, this volume includes some problems in potential theory which were presented in the Problem Session at Hanstholm.

Author : Lester L. Helms
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 47,7 Mb
Release : 2014-04-10
Category : Mathematics
ISBN : 9781447164227

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Potential Theory by Lester L. Helms Pdf

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.

Author : Corneliu Constantinescu,Aurel Cornea
Publisher : Springer
Page : 0 pages
File Size : 52,6 Mb
Release : 1972
Category : Mathematics
ISBN : 3642654320

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Potential Theory on Harmonic Spaces by Corneliu Constantinescu,Aurel Cornea Pdf

There has been a considerable revival of interest in potential theory during the last 20 years. This is made evident by the appearance of new mathematical disciplines in that period which now-a-days are considered as parts of potential theory. Examples of such disciplines are: the theory of Choquet capacities, of Dirichlet spaces, of martingales and Markov processes, of integral representation in convex compact sets as well as the theory of harmonic spaces. All these theories have roots in classical potential theory. The theory of harmonic spaces, sometimes also called axiomatic theory of harmonic functions, plays a particular role among the above mentioned theories. On the one hand, this theory has particularly close connections with classical potential theory. Its main notion is that of a harmonic function and its main aim is the generalization and unification of classical results and methods for application to an extended class of elliptic and parabolic second order partial differential equations. On the other hand, the theory of harmonic spaces is closely related to the theory of Markov processes. In fact, all important notions and results of the theory have a probabilistic interpretation.

Author : Steven R. Bell
Publisher : CRC Press
Page : 164 pages
File Size : 51,7 Mb
Release : 1992-08-14
Category : Mathematics
ISBN : 084938270X

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The Cauchy Transform, Potential Theory and Conformal Mapping by Steven R. Bell Pdf

The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods. The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.

Author : Anton Savin,Boris Sternin
Publisher : Birkhäuser
Page : 138 pages
File Size : 53,6 Mb
Release : 2017-03-28
Category : Mathematics
ISBN : 9783319517445

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Introduction to Complex Theory of Differential Equations by Anton Savin,Boris Sternin Pdf

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.

Author : International Society for Analysis, Applications, and Computation. Congress
Publisher : World Scientific
Page : 737 pages
File Size : 43,6 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9789812794253

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Progress in Analysis by International Society for Analysis, Applications, and Computation. Congress Pdf

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting. Contents: .: Volume 1: Function Spaces and Fractional Calculus (V I Burenkov & S Samko); Asymptotic Decomposition (Methods of Small Parameters, Averaging Theory) (J A Dubinski); Integral Transforms and Applications (S Saitoh et al.); Analytic Functionals, Hyperfunctions and Generalized Functions (M Morimoto & H Komatsu); Geometric Function Theory (G Kohr & M Kohr); omplex Function Spaces (R Aulaskari & I Laine); Value Distribution Theory and Complex Dynamics (C C Yang); Clifford Analysis (K Grlebeck et al.); Octonions (T Dray & C Monogue); Nonlinear Potential Theory (O Martio); Classical and Fine Potential Theory, Holomorphic and Finely Holomorphic Functions (P Tamrazov); Differential Geometry and Control Theory for PDEs (B Gulliver et al.); Differential Geometry and Quantum Physics (-); Dynamical Systems (B Fiedler); Attractors for Partial Differential Equations (G Raugel); Spectral Theory of Differential Operators (B Vainberg); Pseudodifferential Operators, Quantization and Signal Analysis (M W Wong); Microlocal Analysis (B-W Schulze & M Korey); Volume 2: Complex and Functional Analytic Methods in PDEs (A Cialdea et al.); Geometric Properties of Solutions of PDEs (R Magnanini); Qualitative Properties of Solutions of Hyperbolic and SchrAdinger Equations (M Reissig & K Yagdjian); Homogenization Moving Boundaries and Porous Media (A Bourgeat & R P Gilbert); Constructive Methods in Applied Problems (P Krutitskii); Waves in Complex Media (R P Gilbert & A Wirgin); Nonlinear Waves (I Lasiecka & H Koch); Mathematical Analysis of Problems in Solid Mechanics (K Hackl & X Li); Direct and Inverse Scattering (L Fishman); Inverse Problems (G N Makrakis et al.); Mathematical Methods in Non-Destructive Evaluation and Non-Destructive Testing (A Wirgin); Numerical Methods for PDEs, Systems and Optimization (A Ben-Israel & I Herrera). Readership: Graduate students and researchers in real, complex, numerical analysis, as well as mathematical physics."

Author : Walter K. Hayman,Eleanor F. Lingham
Publisher : Springer Nature
Page : 284 pages
File Size : 53,6 Mb
Release : 2019-09-07
Category : Mathematics
ISBN : 9783030251659

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Research Problems in Function Theory by Walter K. Hayman,Eleanor F. Lingham Pdf

In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’. This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems and results needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.

Author : Isaak Rubinstein,Lev Rubinstein
Publisher : Cambridge University Press
Page : 704 pages
File Size : 45,9 Mb
Release : 1998-04-28
Category : Mathematics
ISBN : 0521558468

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Partial Differential Equations in Classical Mathematical Physics by Isaak Rubinstein,Lev Rubinstein Pdf

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

Author : John W. Morgan,Dusa McDuff,Mohammad Tehrani,Kenji Fukaya,Dominic Joyce
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 44,8 Mb
Release : 2019-04-12
Category : Geometry, Differential
ISBN : 9781470450144

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Virtual Fundamental Cycles in Symplectic Topology by John W. Morgan,Dusa McDuff,Mohammad Tehrani,Kenji Fukaya,Dominic Joyce Pdf

The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces. This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.