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The Resource Variable Lebesgue Spaces and Hyperbolic Systems, by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)

Variable Lebesgue Spaces and Hyperbolic Systems, by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)

Creator
Author
Editor
Contributor
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
Language
eng
Work
Publication
Extent
IX, 170 pages 5 illustrations
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
Isbn
9783034808408
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0840-8
Instance
Label
Variable Lebesgue Spaces and Hyperbolic Systems
Title
Variable Lebesgue Spaces and Hyperbolic Systems
Statement of responsibility
by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov
Creator
Contributor
Author
Editor
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
IT-FiEUI
http://library.link/vocab/creatorName
Cruz-Uribe, David
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorDate
1976-.
http://library.link/vocab/relatedWorkOrContributorName
  • Fiorenza, Alberto.
  • Ruzhansky, M.
  • Wirth, Jens.
  • Tikhonov, Sergey
  • SpringerLink (Online service)
Series statement
  • Advanced Courses in Mathematics - CRM Barcelona,
  • Springer eBooks
Series volume
27
http://library.link/vocab/subjectName
  • Mathematics
  • Integral equations
  • Differential equations, Partial
  • Functions, Special
Label
Variable Lebesgue Spaces and Hyperbolic Systems, by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0840-8
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-0348-0840-8
Dimensions
unknown
Extent
IX, 170 pages 5 illustrations
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034808408
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0840-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1048146554
Label
Variable Lebesgue Spaces and Hyperbolic Systems, by David Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0840-8
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-0348-0840-8
Dimensions
unknown
Extent
IX, 170 pages 5 illustrations
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034808408
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0840-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1048146554

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