The Resource Variable Lebesgue spaces and hyperbolic systems, David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)

Variable Lebesgue spaces and hyperbolic systems, David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)

Label
Variable Lebesgue spaces and hyperbolic systems
Title
Variable Lebesgue spaces and hyperbolic systems
Statement of responsibility
David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
Contributor
Author
Subject
Language
eng
Summary
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition
Member of
Cataloging source
GW5XE
Dewey number
515/.43
Illustrations
illustrations
Index
no index present
LC call number
QA312
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Advanced courses in mathematics, CRM Barcelona
Series volume
27
Label
Variable Lebesgue spaces and hyperbolic systems, David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
http://library.link/vocab/branchCode
  • net
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Part I: Introduction to the Variable Lebesgue Spaces -- Introduction and motivation -- Properties of variable Lebesgue spaces -- The Hardy-Littlewood maximal operator -- Extrapolation in variable Lebesgue spaces -- Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems -- Equations with constant coefficients -- Some interesting model cases -- Time-dependent hyperbolic systems -- Effective lower order perturbations -- Examples and counter-examples -- Related topics
Control code
ocn885199538
Dimensions
unknown
Extent
1 online resource (170 pages)
File format
unknown
Form of item
online
Isbn
9783034808408
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0840-8
Other physical details
illustrations
Quality assurance targets
not applicable
http://library.link/vocab/recordID
.b31757868
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)885199538
  • springer3034808399

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
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