Sobolev Spaces On Domains
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Sobolev Spaces On Domains
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Author : Victor I. Burenkov
language : de
Publisher: Springer-Verlag
Release Date : 2013-07-02
Sobolev Spaces On Domains written by Victor I. Burenkov and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains
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Author : Mikhail S. Agranovich
language : en
Publisher: Springer
Release Date : 2015-05-06
Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains written by Mikhail S. Agranovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-06 with Mathematics categories.
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.
Sobolev Spaces In Mathematics Ii
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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-26
Sobolev Spaces In Mathematics Ii written by Vladimir Maz'ya 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 2008-11-26 with Mathematics categories.
Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains
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Author : Mikhail S. Agranovich
language : en
Publisher:
Release Date : 2015
Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains written by Mikhail S. Agranovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
Differentiable Functions On Bad Domains
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Author : Vladimir G Maz'ya
language : en
Publisher: World Scientific
Release Date : 1998-01-15
Differentiable Functions On Bad Domains written by Vladimir G Maz'ya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-15 with Mathematics categories.
The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state. In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given. Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications. This book will be interesting not only to specialists in analysis but also to postgraduate students. Contents:Introduction to Sobolev Spaces for Domains:Basic Properties of Sobolev SpacesExamples of “Bad” Domains in the Theory of Sobolev SpaceSobolev Spaces for Domains Depending on Parameters:Extension of Functions Defined on Parameter Dependent DomainsBoundary Values of Functions with First Derivatives Lp on Parameter Dependent DomainsSobolev Spaces for Domains with Cusps:Extension of Functions to the Exterior of a Domain with the Vertex of a Peak on the BoundaryBoundary Values of Sobolev Functions on Non-Lipschitz Domains Bounded by Lipschitz SurfacesBoundary Values of Functions in Sobolev Spaces for Domains with PeaksImbedding and Trace Theorems for Domains with Outer Peaks and for General Domains Readership: Mathematicians. keywords:Sobolev Spaces;Domains with Cusps;Imbedding and Extension Theorems;Boundary Values of Functions “… the book may be useful and interesting for mathematicians working in other related areas, such as the rest of PDE theory, the calculus of variations, numerical analysis and the theory of functions of several real variables … The book is strongly recommended to researchers and advanced students.” European Mathematical Society Newsletter
Sobolev Spaces
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Author : Robert A. Adams
language : en
Publisher: Elsevier
Release Date : 2003-06-26
Sobolev Spaces written by Robert A. Adams and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike. Self-contained and accessible for readers in other disciplines Written at elementary level making it accessible to graduate students
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.
Sobolev Spaces
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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-11
Sobolev Spaces written by Vladimir Maz'ya 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 2011-02-11 with Mathematics categories.
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.
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.
Lectures On The L2 Sobolev Theory Of The D Bar Neumann Problem
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Author : Emil J. Straube
language : en
Publisher: European Mathematical Society
Release Date : 2010
Lectures On The L2 Sobolev Theory Of The D Bar Neumann Problem written by Emil J. Straube 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 2010 with Mathematics categories.
This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.