Orlicz-Sobolev Spaces on Metric Measure Spaces
Author | : Heli Tuominen |
Publisher | : |
Total Pages | : 96 |
Release | : 2004 |
Genre | : Functional equations |
ISBN | : |
Download Orlicz-Sobolev Spaces on Metric Measure Spaces Book in PDF, Epub and Kindle
Download Orlicz Sobolev Spaces On Metric Measure Spaces full books in PDF, epub, and Kindle. Read online free Orlicz Sobolev Spaces On Metric Measure Spaces ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Heli Tuominen |
Publisher | : |
Total Pages | : 96 |
Release | : 2004 |
Genre | : Functional equations |
ISBN | : |
Author | : Juha Heinonen |
Publisher | : Cambridge University Press |
Total Pages | : 447 |
Release | : 2015-02-05 |
Genre | : Mathematics |
ISBN | : 1316241033 |
Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincaré inequalities.
Author | : Juha Heinonen |
Publisher | : Cambridge University Press |
Total Pages | : 447 |
Release | : 2015-02-05 |
Genre | : Mathematics |
ISBN | : 1107092345 |
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Author | : Vladimir Maz'ya |
Publisher | : Springer Science & Business Media |
Total Pages | : 395 |
Release | : 2008-12-02 |
Genre | : Mathematics |
ISBN | : 038785648X |
This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Author | : Juha Heinonen |
Publisher | : Springer Science & Business Media |
Total Pages | : 149 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461301319 |
The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.
Author | : Petteri Harjulehto |
Publisher | : |
Total Pages | : 25 |
Release | : 2004 |
Genre | : |
ISBN | : |
Author | : Vladimir Maz'ya |
Publisher | : Springer |
Total Pages | : 506 |
Release | : 2013-12-21 |
Genre | : Mathematics |
ISBN | : 3662099225 |
The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Author | : Ari Laptev |
Publisher | : Springer Science & Business Media |
Total Pages | : 414 |
Release | : 2009-12-02 |
Genre | : Mathematics |
ISBN | : 1441913416 |
The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.
Author | : Petteri Harjulehto |
Publisher | : Springer |
Total Pages | : 169 |
Release | : 2019-05-07 |
Genre | : Mathematics |
ISBN | : 303015100X |
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.