Boundary Value Problems In The Spaces Of Distributions
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Boundary Value Problems In The Spaces Of Distributions
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Author : Y. Roitberg
language : en
Publisher: Springer
Release Date : 2014-03-14
Boundary Value Problems In The Spaces Of Distributions written by Y. Roitberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-14 with Mathematics categories.
Elliptic Boundary Value Problems In The Spaces Of Distributions
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Author : Y. Roitberg
language : en
Publisher:
Release Date : 2014-01-15
Elliptic Boundary Value Problems In The Spaces Of Distributions written by Y. Roitberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
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.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
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Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. This first volume is devoted to domains whose boundary is smooth in the neighborhood of finitely many conical points. In particular, the theory encompasses the important case of domains with small holes. The second volume, on the other hand, treats perturbations of the boundary in higher dimensions as well as nonlocal perturbations. The core of this book consists of the solution of general elliptic boundary value problems by complete asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. The construction of this method capitalizes on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Much attention is paid to concrete problems in mathematical physics, for example in elasticity theory. In particular, a study of the asymptotic behavior of stress intensity factors, energy integrals and eigenvalues is presented. To a large extent the book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii
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Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, this second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this book are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Green S Functions And Boundary Value Problems
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Author : Ivar Stakgold
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Green S Functions And Boundary Value Problems written by Ivar Stakgold and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
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.
A Course In Distribution Theory And Applications
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Author : R. S. Pathak
language : en
Publisher: CRC Press
Release Date : 2001
A Course In Distribution Theory And Applications written by R. S. Pathak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The book covers important topics: basic properties of distributions, convolution, Fourier transforms, Sobolev spaces, weak solutions, distributions on locally convex spaces and on differentiable manifolds. It is a largely self-contained text.".
Boundary Value Problems In The Spaces Of Distributions
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Author : Yakov Roitberg
language : en
Publisher: Springer
Release Date : 1999-10-31
Boundary Value Problems In The Spaces Of Distributions written by Yakov Roitberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-31 with Mathematics categories.
This monograph presents elliptic, parabolic and hyperbolic boundary value problems for systems of mixed orders (Douglis-Nirenberg systems). For these problems the `theorem on complete collection of isomorphisms' is proven. Several applications in elasticity and hydrodynamics are treated. The book requires familiarity with the elements of functional analysis, the theory of partial differential equations, and the theory of generalized functions. Audience: This work will be of interest to graduate students and research mathematicians involved in areas such as functional analysis, partial differential equations, operator theory, the mathematics of mechanics, elasticity and viscoelasticity.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions 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 2012-12-06 with Mathematics categories.
In Volumes 1 and 2, we studied, for particular classes of systems {[capital italic]P, [capital italic]Q[lowercase italic subscript]j}, problems in classes of Sobolev spaces (in general constructed starting from [capital italic]L2) of positive integer or (by interpolation) non-integer order; then, by transposition, in classes of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of infinitely differentiable or analytic functions or of Gevrey-type functions and by duality, in spaces of distributions, of analytic functionals or of Gevrey-type ultra-distributions. In this manner, we obtain a clear vision (at least we hope so) of the various possible formulations of the boundary value problems for the systems {[capital italic]P, [capital italic]Q[lowercase italic subscript]j} considered here.