Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation /
.
Bookmark this Record
Catalogue Record 44739
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 44739
.
Reviews
Catalogue Record 44739
.
British Library
Resolver for RSN-44739
Google Scholar
Resolver for RSN-44739
WorldCat
Resolver for RSN-44739
Catalogo Nazionale SBN
Resolver for RSN-44739
GoogleBooks
Resolver for RSN-44739
ICTP Library
Resolver for RSN-44739
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515.96
Title
Weakly Differentiable Functions ([EBook] :) : Sobolev Spaces and Functions of Bounded Variation / / by William P. Ziemer.
Author
Ziemer, William P.
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : : Springer New York : : Imprint: Springer, , 1989.
Physical Details
XVI, 308 p. : online resource.
Series
Graduate texts in mathematics
0072-5285 ; ; 120
ISBN
9781461210153
Summary Note
The term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func tions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions.:
Contents note
1 Preliminaries -- 1.1 Notation -- 1.2 Measures on Rn -- 1.3 Covering Theorems -- 1.4 Hausdorff Measure -- 1.5 Lp-Spaces -- 1.6 Regularization -- 1.7 Distributions -- 1.8 Lorentz Spaces -- Exercises -- Historical Notes -- 2 Sobolev Spaces and Their Basic Properties -- 2.1 Weak Derivatives -- 2.2 Change of Variables for Sobolev Functions -- 2.3 Approximation of Sobolev Functions by Smooth Functions -- 2.4 Sobolev Inequalities -- 2.5 The Rellich-Kondrachov Compactness Theorem -- 2.6 Bessel Potentials and Capacity -- 2.7 The Best Constant in the Sobolev Inequality -- 2.8 Alternate Proofs of the Fundamental Inequalities -- 2.9 Limiting Cases of the Sobolev Inequality -- 2.10 Lorentz Spaces, A Slight Improvement -- Exercises -- Historical Notes -- 3 Pointwise Behavior of Sobolev Functions -- 3.1 Limits of Integral Averages of Sobolev Functions -- 3.2 Densities of Measures -- 3.3 Lebesgue Points for Sobolev Functions -- 3.4 LP-Derivatives for Sobolev Functions -- 3.5 Properties of Lp-Derivatives -- 3.6 An Lp-Version of the Whitney Extension Theorem -- 3.7 An Observation on Differentiation -- 3.8 Rademacher’s Theorem in the Lp-Context -- 3.9 The Implications of Pointwise Differentiability -- 3.10 A Lusin-Type Approximation for Sobolev Functions -- 3.11 The Main Approximation -- Exercises -- Historical Notes -- 4 Poincaré Inequalities—A Unified Approach -- 4.1 Inequalities in a General Setting -- 4.2 Applications to Sobolev Spaces -- 4.3 The Dual of WM,p(?) -- 4.4 Some Measures in (W0M,p(?))* -- 4.5 Poincaré Inequalities -- 4.6 Another Version of Poincaré’s Inequality -- 4.7 More Measures in (WM,p(?))* -- 4.8 Other Inequalities Involving Measures in (WM,p)* -- 4.9 The Case p= 1 -- Exercises -- Historical Notes -- 5 Functions of Bounded Variation -- 5.1 Definitions -- 5.2 Elementary Properties of BV Functions -- 5.3 Regularization of BV Functions -- 5.4 Sets of Finite Perimeter -- 5.5 The Generalized Exterior Normal -- 5.6 Tangential Properties of the Reduced Boundary and the Measure-Theoretic Normal -- 5.7 Rectifiability of the Reduced Boundary -- 5.8 The Gauss-Green Theorem -- 5.9 Pointwise Behavior of BV Functions -- 5.10 The Trace of a BV Function -- 5.11 Sobolev-Type Inequalities for BV Functions -- 5.12 Inequalities Involving Capacity -- 5.13 Generalizations to the Case p> 1 -- 5.14 Trace Defined in Terms of Integral Averages -- Exercises -- Historical Notes -- List of Symbols.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4612-1015-3
Links to Related Works
Subject References:
Mathematics
.
Potential Theory
.
Potential theory (Mathematics)
.
Authors:
Ziemer, William P.
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Graduate texts in mathematics
.
GTM
.
Classification:
515.96
.
.
ISBD Display
Catalogue Record 44739
.
Tag Display
Catalogue Record 44739
.
Related Works
Catalogue Record 44739
.
Marc XML
Catalogue Record 44739
.
Add Title to Basket
Catalogue Record 44739
.
Catalogue Information 44739
Beginning of record
.
Catalogue Information 44739
Top of page
.
Download Title
Catalogue Record 44739
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
44739
1
44739
-
2
44739
-
3
44739
-
4
44739
-
5
44739
-
Quick Search
Search for