The Resource Variable Lebesgue Spaces and Hyperbolic Systems, by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
Variable Lebesgue Spaces and Hyperbolic Systems, by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
Resource Information
The item Variable Lebesgue Spaces and Hyperbolic Systems, by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Variable Lebesgue Spaces and Hyperbolic Systems, by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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 nonstandard 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 HardyLittlewood 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 selfcontained, 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 timedependent 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 timedependent 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 timefrequency 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
 Extent
 IX, 170 pages 5 illustrations
 Contents

 Part I: Introduction to the Variable Lebesgue Spaces
 Introduction and motivation
 Properties of variable Lebesgue spaces
 The HardyLittlewood 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
 Timedependent hyperbolic systems
 Effective lower order perturbations
 Examples and counterexamples
 Related topics
 Isbn
 9783034808408
 Label
 Variable Lebesgue Spaces and Hyperbolic Systems
 Title
 Variable Lebesgue Spaces and Hyperbolic Systems
 Statement of responsibility
 by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov
 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 nonstandard 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 HardyLittlewood 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 selfcontained, 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 timedependent 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 timedependent 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 timefrequency 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
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorName
 CruzUribe, 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 CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
 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 HardyLittlewood 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  Timedependent hyperbolic systems  Effective lower order perturbations  Examples and counterexamples  Related topics
 Control code
 9783034808408
 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, noncommercial 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
 10.1007/9783034808408
 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 CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)
 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 HardyLittlewood 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  Timedependent hyperbolic systems  Effective lower order perturbations  Examples and counterexamples  Related topics
 Control code
 9783034808408
 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, noncommercial 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
 10.1007/9783034808408
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/VariableLebesgueSpacesandHyperbolicSystems/F6ZrgG0lXyU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/VariableLebesgueSpacesandHyperbolicSystems/F6ZrgG0lXyU/">Variable Lebesgue Spaces and Hyperbolic Systems, by David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; edited by Sergey Tikhonov, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>