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

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

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
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
CDX
http://library.link/vocab/creatorName
Cruz-Uribe, 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 Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
Instantiates
Publication
Copyright
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 Cruz-Uribe and Alberto Fiorenza -- Introduction and motivation -- Properties of variable Lebesgue spaces -- The Hardy-Littlewood 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 -- Time-dependent hyperbolic systems -- Effective lower order perturbations -- Examples and counter-examples -- 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 Cruz-Uribe, Alberto Fiorenza, Michael Ruzhansky, Jens Wirth ; editor for this volume: Sergey Tikhonov
Publication
Copyright
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 Cruz-Uribe and Alberto Fiorenza -- Introduction and motivation -- Properties of variable Lebesgue spaces -- The Hardy-Littlewood 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 -- Time-dependent hyperbolic systems -- Effective lower order perturbations -- Examples and counter-examples -- 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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