Maximal Function Methods For Sobolev Spaces
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Maximal Function Methods For Sobolev Spaces
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Author : Juha Kinnunen
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-02
Maximal Function Methods For Sobolev Spaces written by Juha Kinnunen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Education categories.
This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Hopf Algebras And Galois Module Theory
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Author : Lindsay N. Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-10
Hopf Algebras And Galois Module Theory written by Lindsay N. Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Education categories.
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1985
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Aeronautics categories.
Theory Of Function Spaces
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Author : Hans Triebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-16
Theory Of Function Spaces written by Hans Triebel 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 2010-06-16 with Social Science categories.
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where ‐∞s∞ and 0p,q≤∞, which include many classical and modern spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rsubn
Fine Regularity Of Solutions Of Elliptic Partial Differential Equations
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Author : Jan Malý
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Fine Regularity Of Solutions Of Elliptic Partial Differential Equations written by Jan Malý and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
Harmonic Analysis Methods In Partial Differential Equations
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Author : Changxing Miao
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-06-02
Harmonic Analysis Methods In Partial Differential Equations written by Changxing Miao and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-02 with Mathematics categories.
This volume applies theories of harmonic analysis to the study of nonlinear partial differential equations. It covers consolidation characterizations of differentiable function spaces, and the theory of three generations of C-Z singular integral operators, Fourier restriction estimation, Strichartz estimation, and Littlewood-Paley theory. It combines harmonic analysis methods with the study of partial differential equations.
Perverse Sheaves And Applications To Representation Theory
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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-27
Perverse Sheaves And Applications To Representation Theory written by Pramod N. Achar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Education categories.
Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
Sobolev Spaces Of Fractional Order Nemytskij Operators And Nonlinear Partial Differential Equations
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Author : Thomas Runst
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-22
Sobolev Spaces Of Fractional Order Nemytskij Operators And Nonlinear Partial Differential Equations written by Thomas Runst and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-22 with Mathematics categories.
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. Please submit book proposals to Jürgen Appell.
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian
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Author : Pablo Raúl Stinga
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian written by Pablo Raúl Stinga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor. Features Self-contained treatment of the topic Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers. Replete with useful references.
Recovery Methodologies Regularization And Sampling
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Author : Willi Freeden
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-21
Recovery Methodologies Regularization And Sampling written by Willi Freeden 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 2023-08-21 with Mathematics categories.
The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.