Variable Lebesgue spaces and hyperbolic systems
The Resource Variable Lebesgue spaces and hyperbolic systems Label
 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
2 Instances of the Work Variable Lebesgue spaces and hyperbolic systems
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Context of Variable Lebesgue spaces and hyperbolic systemsItems
Instances
 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)
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