The Resource Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
 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
 1 online resource (170 pages)
 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
 David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
 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
 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 CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)
 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 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
 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
 10.1007/9783034808408
 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
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.deakin.edu.au/portal/VariableLebesguespacesandhyperbolicsystems/s1xe86VTXzU/" typeof="CreativeWork http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.deakin.edu.au/portal/VariableLebesguespacesandhyperbolicsystems/s1xe86VTXzU/">Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov 9ICREA and CRM Barcelona)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.library.deakin.edu.au/#Deakin%20University%20Library"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.deakin.edu.au/">Deakin University Library</a></span></span></span></span></div>