Distributions Sobolev Spaces Elliptic Equations

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Distributions Sobolev Spaces Elliptic Equations

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Author : Dorothee Haroske
language : en
Publisher: European Mathematical Society
Release Date : 2007

Distributions Sobolev Spaces Elliptic Equations written by Dorothee Haroske and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.

Distributions Sobolev Spaces Elliptic Equations

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Author : DOROTHEE D. HAROSKE; HANS TRIEBEL.
language : en
Publisher:
Release Date :

Distributions Sobolev Spaces Elliptic Equations written by DOROTHEE D. HAROSKE; HANS TRIEBEL. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Functional Spaces For The Theory Of Elliptic Partial Differential Equations

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Author : Françoise Demengel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-24

Functional Spaces For The Theory Of Elliptic Partial Differential Equations written by Françoise Demengel 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 2012-01-24 with Mathematics categories.

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.

Theory Of Function Spaces Iv

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Author : Hans Triebel
language : en
Publisher: Springer Nature
Release Date : 2020-01-23

Theory Of Function Spaces Iv written by Hans Triebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Mathematics categories.

This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".

Distributions And Operators

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Author : Gerd Grubb
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-10

Distributions And Operators written by Gerd Grubb 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 2008-10-10 with Mathematics categories.

This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.

Analysis Of Finite Difference Schemes

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Author : Boško S. Jovanović
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-22

Analysis Of Finite Difference Schemes written by Boško S. Jovanović 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 2013-10-22 with Mathematics categories.

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Basic Theory Of Fractional Differential Equations Third Edition

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Author : Yong Zhou
language : en
Publisher: World Scientific
Release Date : 2023-10-06

Basic Theory Of Fractional Differential Equations Third Edition written by Yong Zhou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Mathematics categories.

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Linear Systems Signal Processing And Hypercomplex Analysis

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Author : Daniel Alpay
language : en
Publisher: Springer
Release Date : 2019-08-08

Linear Systems Signal Processing And Hypercomplex Analysis written by Daniel Alpay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-08 with Mathematics categories.

This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.

Sparse Grids And Applications Munich 2012

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Author : Jochen Garcke
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-11

Sparse Grids And Applications Munich 2012 written by Jochen Garcke 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 2014-04-11 with Mathematics categories.

Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.

Numerical Methods And Analysis Of Multiscale Problems

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Author : Alexandre L. Madureira
language : en
Publisher: Springer
Release Date : 2017-02-15

Numerical Methods And Analysis Of Multiscale Problems written by Alexandre L. Madureira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-15 with Mathematics categories.

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.