Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains
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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.
Sharp Boundary Trace Theory And Schr Dinger Operators On Bounded Lipschitz Domains
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Author : Jussi Behrndt
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-02
Sharp Boundary Trace Theory And Schr Dinger Operators On Bounded Lipschitz Domains written by Jussi Behrndt and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-02 with Mathematics categories.
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Analysis As A Life
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Author : Sergei Rogosin
language : en
Publisher: Springer
Release Date : 2019-01-30
Analysis As A Life written by Sergei Rogosin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Mathematics categories.
This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).
Variational Techniques For Elliptic Partial Differential Equations
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Author : Francisco J. Sayas
language : en
Publisher: CRC Press
Release Date : 2019-01-16
Variational Techniques For Elliptic Partial Differential Equations written by Francisco J. Sayas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-16 with Mathematics categories.
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
From Complex Analysis To Operator Theory A Panorama
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Author : Malcolm Brown
language : en
Publisher: Springer Nature
Release Date : 2023-09-21
From Complex Analysis To Operator Theory A Panorama written by Malcolm Brown and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-21 with Mathematics categories.
This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.
Hilbert Space Splittings And Iterative Methods
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Author : Michael Griebel
language : en
Publisher: Springer Nature
Release Date : 2024-11-06
Hilbert Space Splittings And Iterative Methods written by Michael Griebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller, finite-dimensional) Hilbert spaces $V_i$ in a certain order, combining them, and using the combined approximations in an iterative procedure. The spaces $V_i$ form a so-called space splitting for V, they need not necessarily be subspaces of V, and their number can be finite or infinite. The convergence behavior of Schwarz methods is influenced by certain properties of the space splittings they are based on. These properties are identified, and a detailed treatment of traditional deterministic and more recent greedy and stochastic orderings in the subproblem solution process is given, together with an investigation of accelerated methods. To illustrate the abstract theory, the numerical linear algebra analogs of the iterative methods covered in the book are discussed. Its standard application to the convergence theory of multilevel and domain decomposition methods for solving PDE problems is explained, and links to optimization theory and online learning algorithms are given. Providing an introduction and overview of iterative methods which are based on problem decompositions and suitable for parallel and distributed computing, the book could serve as the basis for a one- or two-semester course for M.S. and Ph.D. students specializing in numerical analysis and scientific computing. It will also appeal to a wide range of researchers interested in scientific computing in the broadest sense.
Integral Methods In Science And Engineering
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Author : Christian Constanda
language : en
Publisher: Springer Nature
Release Date : 2023-10-31
Integral Methods In Science And Engineering written by Christian Constanda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-31 with Mathematics categories.
This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.
Boundary Value Problems Weyl Functions And Differential Operators
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Author : Jussi Behrndt
language : en
Publisher: Springer Nature
Release Date : 2020-01-03
Boundary Value Problems Weyl Functions And Differential Operators written by Jussi Behrndt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Inverse Problems For Mechanical Systems
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Author : Antonino Morassi
language : en
Publisher: Springer Nature
Release Date : 2025-06-13
Inverse Problems For Mechanical Systems written by Antonino Morassi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-13 with Science categories.
This book explores the crucial role of inverse problems across various fields of applied science and technology. By examining physical phenomena governed by mathematical physics, it addresses the challenge of determining unknown parameters and developing non-destructive methods for systems of solid and structural mechanics. It delves into the inherent mathematical complexities of inverse problems and presents innovative strategies for overcoming these issues. Aimed at doctoral students and researchers in civil and mechanical engineering, mathematical physics, and applied mathematics, the book provides a solid theoretical foundation and equips readers with the necessary mathematical and computational tools to tackle diverse inverse problems.
An Invitation To Unbounded Representations Of Algebras On Hilbert Space
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Author : Konrad Schmüdgen
language : en
Publisher: Springer Nature
Release Date : 2020-07-28
An Invitation To Unbounded Representations Of Algebras On Hilbert Space written by Konrad Schmüdgen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-28 with Mathematics categories.
This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.