The Resource Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
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The item Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
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,169 pages
 Contents

 Introduction to the variable Lebesgue spaces / David CruzUribe and Alberto Fiorenza
 Introduction and motivation
 Properties of variable Lebesgue spaces
 The HardyLittlewood maximal operator
 Extrapolation in variable Lebesgue spaces
 Asymptotic behaviour of solutions to hyperbolic equations and systems / Michael Ruzhansky and Jens Wirth
 Introduction
 Equations with constant coefficients
 Some interesting model cases
 Timedependent hyperbolic systems
 Effective lower order perturbations
 Examples and counterexamples
 Related topics
 Isbn
 9783034808392
 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
 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
 CDX
 http://library.link/vocab/creatorName
 CruzUribe, David V
 Dewey number
 515.43
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA312
 LC item number
 .C778 2014
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1976
 http://library.link/vocab/relatedWorkOrContributorName

 Fiorenza, Alberto
 Ruzhansky, M.
 Wirth, Jens
 Tikhonov, Sergey
 Series statement
 Advanced courses in mathematics, CRM Barcelona
 http://library.link/vocab/subjectName

 Lebesgue integral
 Differential equations, Hyperbolic
 Label
 Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
 Bibliography note
 Includes bibliographical references
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction to the variable Lebesgue spaces / David CruzUribe and Alberto Fiorenza  Introduction and motivation  Properties of variable Lebesgue spaces  The HardyLittlewood maximal operator  Extrapolation in variable Lebesgue spaces  Asymptotic behaviour of solutions to hyperbolic equations and systems / Michael Ruzhansky and Jens Wirth  Introduction  Equations with constant coefficients  Some interesting model cases  Timedependent hyperbolic systems  Effective lower order perturbations  Examples and counterexamples  Related topics
 Control code
 889554931
 Dimensions
 25 cm.
 Extent
 ix,169 pages
 Isbn
 9783034808392
 Isbn Type
 (pbk.)
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (OCoLC)889554931
 Label
 Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
 Bibliography note
 Includes bibliographical references
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction to the variable Lebesgue spaces / David CruzUribe and Alberto Fiorenza  Introduction and motivation  Properties of variable Lebesgue spaces  The HardyLittlewood maximal operator  Extrapolation in variable Lebesgue spaces  Asymptotic behaviour of solutions to hyperbolic equations and systems / Michael Ruzhansky and Jens Wirth  Introduction  Equations with constant coefficients  Some interesting model cases  Timedependent hyperbolic systems  Effective lower order perturbations  Examples and counterexamples  Related topics
 Control code
 889554931
 Dimensions
 25 cm.
 Extent
 ix,169 pages
 Isbn
 9783034808392
 Isbn Type
 (pbk.)
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number
 (OCoLC)889554931
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/VariableLebesguespacesandhyperbolicsystems/sfH6gUmPWOg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/VariableLebesguespacesandhyperbolicsystems/sfH6gUmPWOg/">Variable Lebesgue spaces and hyperbolic systems, David CruzUribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>