Differentiable Functions On Bad Domains
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Differentiable Functions On Bad Domains
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Author : V. G. Maz?i?a
language : en
Publisher: World Scientific
Release Date : 1997
Differentiable Functions On Bad Domains written by V. G. Maz?i?a and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The spaces of functions with derivatives in p, 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.
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.
Perspectives In Partial Differential Equations Harmonic Analysis And Applications
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Author : Dorina Mitrea
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Perspectives In Partial Differential Equations Harmonic Analysis And Applications written by Dorina Mitrea 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 2008 with Mathematics categories.
This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Analysis Partial Differential Equations And Applications
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Author : Alberto Cialdea
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-14
Analysis Partial Differential Equations And Applications written by Alberto Cialdea 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 2010-01-14 with Mathematics categories.
This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.
Harmonic Analysis And Partial Differential Equations
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Author : Anatoly Golberg
language : en
Publisher: Springer Nature
Release Date : 2023-03-25
Harmonic Analysis And Partial Differential Equations written by Anatoly Golberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-25 with Mathematics categories.
Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
The Maz Ya Anniversary Collection
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Author : Jürgen Rossmann
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
The Maz Ya Anniversary Collection written by Jürgen Rossmann 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 1999 with Mathematics categories.
This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.
Function Spaces And Partial Differential Equations
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Author : Ali Taheri
language : en
Publisher: OUP Oxford
Release Date : 2015-07-30
Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
Dirichlet Dirichlet Domain Decomposition Methods For Elliptic Problems H And Hp Finite Element Discretizations
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Author : Vadim Glebiovich Korneev
language : en
Publisher: World Scientific
Release Date : 2015-01-29
Dirichlet Dirichlet Domain Decomposition Methods For Elliptic Problems H And Hp Finite Element Discretizations written by Vadim Glebiovich Korneev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-29 with Mathematics categories.
Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.
Elliptic Equations In Polyhedral Domains
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Author : V. G. Maz_i_a
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-04-22
Elliptic Equations In Polyhedral Domains written by V. G. Maz_i_a 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 2010-04-22 with Mathematics categories.
This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.
H Lder And Locally H Lder Continuous Functions And Open Sets Of Class C K C K Lambda
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Author : Renato Fiorenza
language : en
Publisher: Birkhäuser
Release Date : 2017-01-13
H Lder And Locally H Lder Continuous Functions And Open Sets Of Class C K C K Lambda written by Renato Fiorenza and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-13 with Mathematics categories.
This book offers a systematic treatment of a classic topic in Analysis. It fills a gap in the existing literature by presenting in detail the classic λ-Hölder condition and introducing the notion of locally Hölder-continuous function in an open set Ω in Rn. Further, it provides the essential notions of multidimensional geometry applied to analysis. Written in an accessible style and with proofs given as clearly as possible, it is a valuable resource for graduate students in Mathematical Analysis and researchers dealing with Hölder-continuous functions and their applications.