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Approximately Analytic Functions Of Bounded Type And Boundary Behaviour Of Solutions Of Elliptic Partial Differential Equations
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Book Synopsis Approximately Analytic Functions of Bounded Type and Boundary Behaviour of Solutions of Elliptic Partial Differential Equations by : Harold Hsiao-li Chang
Download or read book Approximately Analytic Functions of Bounded Type and Boundary Behaviour of Solutions of Elliptic Partial Differential Equations written by Harold Hsiao-li Chang and published by . This book was released on 1951 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form by : Abubakar Mwasa
Download or read book Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form written by Abubakar Mwasa and published by Linköping University Electronic Press. This book was released on 2021-02-23 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis consists of three papers focussing on the study of nonlinear elliptic partial differential equations in a nonempty open subset Ω of the n-dimensional Euclidean space Rn. We study the existence and uniqueness of the solutions, as well as their behaviour near the boundary of Ω. The behaviour of the solutions at infinity is also discussed when Ω is unbounded. In Paper A, we consider a mixed boundary value problem for the p-Laplace equation ∆pu := div(|∇u| p−2∇u) = 0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. By a suitable transformation of the independent variables, this mixed problem is transformed into a Dirichlet problem for a degenerate (weighted) elliptic equation on a bounded set. By analysing the transformed problem in weighted Sobolev spaces, it is possible to obtain the existence of continuous weak solutions to the mixed problem, both for Sobolev and for continuous data on the Dirichlet part of the boundary. A characterisation of the boundary regularity of the point at infinity is obtained in terms of a new variational capacity adapted to the cylinder. In Paper B, we study Perron solutions to the Dirichlet problem for the degenerate quasilinear elliptic equation div A(x, ∇u) = 0 in a bounded open subset of Rn. The vector-valued function A satisfies the standard ellipticity assumptions with a parameter 1 < p < ∞ and a p-admissible weight w. For general boundary data, the Perron method produces a lower and an upper solution, and if they coincide then the boundary data are called resolutive. We show that arbitrary perturbations on sets of weighted p-capacity zero of continuous (and quasicontinuous Sobolev) boundary data f are resolutive, and that the Perron solutions for f and such perturbations coincide. As a consequence, it is also proved that the Perron solution with continuous boundary data is the unique bounded continuous weak solution that takes the required boundary data outside a set of weighted p-capacity zero. Some results in Paper C are a generalisation of those in Paper A, extended to quasilinear elliptic equations of the form div A(x, ∇u) = 0. Here, results from Paper B are used to prove the existence and uniqueness of continuous weak solutions to the mixed boundary value problem for continuous Dirichlet data. Regularity of the boundary point at infinity for the equation div A(x, ∇u) = 0 is characterised by a Wiener type criterion. We show that sets of Sobolev p-capacity zero are removable for the solutions and also discuss the behaviour of the solutions at ∞. In particular, a certain trichotomy is proved, similar to the Phragmén–Lindelöf principle.
Book Synopsis Partial Differential and Integral Equations by : Heinrich Begehr
Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Book Synopsis N-Dimensional Quasiconformal (QCf) Mappings by : Petru Caraman
Download or read book N-Dimensional Quasiconformal (QCf) Mappings written by Petru Caraman and published by CRC Press. This book was released on 1974 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathema tics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclo paedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reason ably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of pre cise theorems with detailed definitions and technical details on how to carry out proofs and con structions.
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by : Guo Chun Wen
Download or read book Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy written by Guo Chun Wen and published by World Scientific. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fishing community of Fjallbacka, life is remote, peaceful, and for some, tragically short. Foul play was always suspected in the disappearance twenty years ago of two young campers, but their bodies were never found. But now, a young boy out playing has confirmed the grim truth. Their remains are discovered alongside those of a fresh victim, sending the tiny town into shock. Local detective Patrik Hedstrom, expecting a baby with his girlfriend Erica, can only imagine what it is like to lose a child. When a second young girl goes missing, Hedstrom's attention focuses on the Hults, a feuding clan of misfits, religious fanatics and criminals. The suspect list is long but time is short which of this family's dark secrets will provide the vital clue? Praise for The Ice Princess : The hottest crime genre of the moment is Nordic noir and Swedish writer Camilla Luckberg (who shares Stieg Larsson's translator) is one of the reasons. As with all Scandinavian murder mysteries, it's darker, bleaker, and the plot far more sinister than similar American fare. Larsson fans who give Luckberg's novel a chance to seduce them will be rewarded. USA Today At the start of Luckberg's haunting U.S. debut, biographer Erica Falck feels compelled to write a novel about why her beautiful friend Alex would kill herself. Luckberg skillfully details how horrific secrets are never completely buried and how silence can kill the soul." Publishers Weekly , starred review Camilla Luckberg has written seven blockbuster novels in her native Swedish but, until now, no one has published any of them in the United States. Now Pegasus Books has stepped forward.â¿ â¿¿ The New York Times Heart-stopping a masterclass in Scandinavian crime fiction." Val McDermid
Book Synopsis Plane Waves and Spherical Means by : F. John
Download or read book Plane Waves and Spherical Means written by F. John and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form. New Rochelle FRITZ JOHN September, 1955 [v] CONTENTS Introduction. . . . . . . 1 CHAPTER I Decomposition of an Arbitrary Function into Plane Waves Explanation of notation . . . . . . . . . . . . . . . 7 The spherical mean of a function of a single coordinate. 7 9 Representation of a function by its plane integrals . CHAPTER II Tbe Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients Hyperbolic equations. . . . . . . . . . . . . . . . . . . . . . 15 Geometry of the normal surface for a strictly hyperbolic equation. 16 Solution of the Cauchy problem for a strictly hyperbolic equation . 20 Expression of the kernel by an integral over the normal surface. 23 The domain of dependence . . . . . . . . . . . . . . . . . . . 29 The wave equation . . . . . . . . . . . . . . . . . . . . . . 32 The initial value problem for hyperbolic equations with a normal surface having multiple points . . . . . . . . . . . . . . . . . . . . 36 CHAPTER III The Fundamental Solution of a Linear Elliptic Differential Equation witL Analytic Coefficients Definition of a fundamental solution . . . . . . . . . . . . . . 43 The Cauchy problem . . . . . . . . . . . . . . . . . . . . . 45 Solution of the inhomogeneous equation with a plane wave function as right hand side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 The fundamental solution. . . . . . . . . . . . . . . . . . . . . .
Book Synopsis Comprehensive Dissertation Index, 1861-1972: Mathematics and statistics by : Xerox University Microfilms
Download or read book Comprehensive Dissertation Index, 1861-1972: Mathematics and statistics written by Xerox University Microfilms and published by . This book was released on 1973 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Comprehensive Dissertation Index by :
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1973 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Publisher :World Scientific ISBN 13 : Total Pages :820 pages Book Rating :4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Emerging Problems in the Homogenization of Partial Differential Equations by : Patrizia Donato
Download or read book Emerging Problems in the Homogenization of Partial Differential Equations written by Patrizia Donato and published by Springer Nature. This book was released on 2021-02-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.
Book Synopsis Bibliography of Mathematics Published in Communist China During the Period 1949-1960 by :
Download or read book Bibliography of Mathematics Published in Communist China During the Period 1949-1960 written by and published by . This book was released on 1961 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixed Type Equations by : John Michael Rassias
Download or read book Mixed Type Equations written by John Michael Rassias and published by . This book was released on 1986 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Book Synopsis Numerical Treatment of Partial Differential Equations by : Christian Grossmann
Download or read book Numerical Treatment of Partial Differential Equations written by Christian Grossmann and published by Springer Science & Business Media. This book was released on 2007-08-11 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
