Search Results for: differential operators on spaces of variable integrability

Author: David E Edmunds
Publisher: World Scientific
Size: 75.13 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 224
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Differential Operators On Spaces Of Variable Integrability Book Description

by David E Edmunds, Differential Operators On Spaces Of Variable Integrability Books available in PDF, EPUB, Mobi Format. Download Differential Operators On Spaces Of Variable Integrability books, The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration. The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered. At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics. Contents:Preliminaries:The Geometry of Banach SpacesSpaces with Variable ExponentSobolev Spaces with Variable Exponent:Definition and Functional-analytic PropertiesSobolev EmbeddingsCompact EmbeddingsRiesz PotentialsPoincaré-type InequalitiesEmbeddingsHölder Spaces with Variable ExponentsCompact Embeddings RevisitedThe p(·)-Laplacian:PreliminariesThe p(·)-LaplacianStability with Respect to IntegrabilityEigenvalues:The Derivative of the ModularCompactness and EigenvaluesModular EigenvaluesStability with Respect to the ExponentConvergence Properties of the EigenfunctionsApproximation on Lp Spaces:s-numbers and n-widthsA Sobolev EmbeddingIntegral Operators Readership: Graduates and researchers interested in differential operators and function spaces. Key Features:Novelty: there is no book covering the principal research topics included in this workExtension: other works give detailed accounts of the basic features of spaces of variable exponents. Our book provides a natural extension to the realm of differential operators on those spacesDepth: new insights are given into differential operators in spaces of variable exponents. In particular, the book will contain novel material on the stability of eigenvalues that has been developed very recentlyKeywords:Lebesgue Spaces with Variable Integrability;Differential Operators;Sobolev Spaces;Eigenvalues;Eigenfunctions

Author: D. E. Edmunds
Publisher: Springer
Size: 61.80 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 322
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Elliptic Differential Operators And Spectral Analysis Book Description

by D. E. Edmunds, Elliptic Differential Operators And Spectral Analysis Books available in PDF, EPUB, Mobi Format. Download Elliptic Differential Operators And Spectral Analysis books, This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.

Author: Osvaldo Mendez
Publisher: CRC Press
Size: 68.97 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 262
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Analysis On Function Spaces Of Musielak Orlicz Type Book Description

by Osvaldo Mendez, Analysis On Function Spaces Of Musielak Orlicz Type Books available in PDF, EPUB, Mobi Format. Download Analysis On Function Spaces Of Musielak Orlicz Type books, Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area

Author: Petteri Harjulehto
Publisher: Springer
Size: 26.25 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 169
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Orlicz Spaces And Generalized Orlicz Spaces Book Description

by Petteri Harjulehto, Orlicz Spaces And Generalized Orlicz Spaces Books available in PDF, EPUB, Mobi Format. Download Orlicz Spaces And Generalized Orlicz Spaces books, This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Author: Decio Levi
Publisher: Cambridge University Press
Size: 39.18 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages :
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Symmetries And Integrability Of Difference Equations Book Description

by Decio Levi, Symmetries And Integrability Of Difference Equations Books available in PDF, EPUB, Mobi Format. Download Symmetries And Integrability Of Difference Equations books, Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.

Author: T.G. Vozmischeva
Publisher: Springer Science & Business Media
Size: 47.95 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 184
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Integrable Problems Of Celestial Mechanics In Spaces Of Constant Curvature Book Description

by T.G. Vozmischeva, Integrable Problems Of Celestial Mechanics In Spaces Of Constant Curvature Books available in PDF, EPUB, Mobi Format. Download Integrable Problems Of Celestial Mechanics In Spaces Of Constant Curvature books, Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.

Author: Boris Kruglikov
Publisher: Springer Science & Business Media
Size: 10.50 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 386
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Differential Equations Geometry Symmetries And Integrability Book Description

by Boris Kruglikov, Differential Equations Geometry Symmetries And Integrability Books available in PDF, EPUB, Mobi Format. Download Differential Equations Geometry Symmetries And Integrability books, The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Author: Yvette Kosmann-Schwarzbach
Publisher: Springer Science & Business Media
Size: 50.34 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 340
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Integrability Of Nonlinear Systems Book Description

by Yvette Kosmann-Schwarzbach, Integrability Of Nonlinear Systems Books available in PDF, EPUB, Mobi Format. Download Integrability Of Nonlinear Systems books, The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Author: Gianni Cassinelli
Publisher: Springer Science & Business Media
Size: 54.97 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 111
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The Theory Of Symmetry Actions In Quantum Mechanics Book Description

by Gianni Cassinelli, The Theory Of Symmetry Actions In Quantum Mechanics Books available in PDF, EPUB, Mobi Format. Download The Theory Of Symmetry Actions In Quantum Mechanics books, This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.

Author: Kiyosi Ito
Publisher: SIAM
Size: 77.47 MB
Format: PDF, ePub, Mobi
Category : Function spaces
Languages : en
Pages : 70
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Foundations Of Stochastic Differential Equations In Infinite Dimensional Spaces Book Description

by Kiyosi Ito, Foundations Of Stochastic Differential Equations In Infinite Dimensional Spaces Books available in PDF, EPUB, Mobi Format. Download Foundations Of Stochastic Differential Equations In Infinite Dimensional Spaces books, A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.