Distributions Sobolev Spaces Elliptic Equations

Author : Dorothee Haroske,Hans Triebel
Publisher : European Mathematical Society
Page : 312 pages
File Size : 52,9 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190426

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Distributions, Sobolev Spaces, Elliptic Equations by Dorothee Haroske,Hans Triebel Pdf

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.

Author : DOROTHEE D. HAROSKE; HANS TRIEBEL.
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 3037195428

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DISTRIBUTIONS, SOBOLEV SPACES, ELLIPTIC EQUATIONS. by DOROTHEE D. HAROSKE; HANS TRIEBEL. Pdf

Author : Hans Triebel
Publisher : Springer Nature
Page : 160 pages
File Size : 41,9 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9783030358914

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Theory of Function Spaces IV by Hans Triebel Pdf

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".

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821846841

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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by Nikolaĭ Vladimirovich Krylov Pdf

This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.

Author : Mikhail S. Agranovich
Publisher : Springer
Page : 331 pages
File Size : 44,6 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319146485

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Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by Mikhail S. Agranovich Pdf

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Author : Françoise Demengel,Gilbert Demengel
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 52,7 Mb
Release : 2012-01-24
Category : Mathematics
ISBN : 9781447128076

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Functional Spaces for the Theory of Elliptic Partial Differential Equations by Françoise Demengel,Gilbert Demengel Pdf

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.

Author : Pulin Kumar Bhattacharyya
Publisher : Walter de Gruyter
Page : 871 pages
File Size : 55,9 Mb
Release : 2012-05-29
Category : Mathematics
ISBN : 9783110269291

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Distributions by Pulin Kumar Bhattacharyya Pdf

This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested in studying the problems of mathematical physics in general and their approximate solutions on computer in particular. Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.

Author : Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell
Publisher : CRC Press
Page : 492 pages
File Size : 41,7 Mb
Release : 2019-01-16
Category : Mathematics
ISBN : 9780429016202

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Variational Techniques for Elliptic Partial Differential Equations by Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell Pdf

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

Author : Y. Roitberg
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401154109

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Elliptic Boundary Value Problems in the Spaces of Distributions by Y. Roitberg Pdf

This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications. It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In the early sixties, Lions and Magenes, and Berezansky, Krein and Roitberg established the theorems on complete collection of isomorphisms. Further progress of the theory was connected with proving the theorem on complete collection of isomorphisms for new classes of problems, and hence with the development of new methods to prove these theorems. The theorems on isomorphisms were first established for elliptic equations with normal boundary conditions. However, after the Noetherian property of elliptic problems was proved without assuming the normality of the boundary expressions, this became the natural way to consider the problems of establishing the theorems on isomorphisms for general elliptic problems. The present author's method of solving this problem enabled proof of the theorem on complete collection of isomorphisms for the operators generated by elliptic boundary-value problems for general systems of equations. Audience: This monograph will be of interest to mathematicians whose work involves partial differential equations, functional analysis, operator theory and the mathematics of mechanics.

Author : Svetlin G. Georgiev
Publisher : Springer
Page : 218 pages
File Size : 53,7 Mb
Release : 2015-07-13
Category : Mathematics
ISBN : 9783319195278

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Theory of Distributions by Svetlin G. Georgiev Pdf

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Author : Thomas Runst,Winfried Sickel
Publisher : Walter de Gruyter
Page : 568 pages
File Size : 41,9 Mb
Release : 1996
Category : Mathematics
ISBN : 3110151138

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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by Thomas Runst,Winfried Sickel Pdf

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dłotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Author : Joseph Wloka
Publisher : Cambridge University Press
Page : 536 pages
File Size : 41,9 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 0521277590

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Partial Differential Equations by Joseph Wloka Pdf

A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.

Author : Adina Chirilă,Marin Marin,Andreas Öchsner
Publisher : Springer Nature
Page : 277 pages
File Size : 54,6 Mb
Release : 2021-02-08
Category : Mathematics
ISBN : 9783030671594

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Distribution Theory Applied to Differential Equations by Adina Chirilă,Marin Marin,Andreas Öchsner Pdf

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method. The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.

Author : Michael Eugene Taylor
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 44,9 Mb
Release : 1996
Category : Mathematics
ISBN : 0387946535

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Partial Differential Equations I by Michael Eugene Taylor Pdf

This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.

Author : Vladimir Maz'ya
Publisher : Springer
Page : 866 pages
File Size : 48,5 Mb
Release : 2011-03-25
Category : Mathematics
ISBN : 3642155650

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Sobolev Spaces by Vladimir Maz'ya Pdf

Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.