The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Author(s): Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Ruzicka (auth.)
Series: Lecture Notes in Mathematics 2017
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 509
Tags: Analysis; Functional Analysis; Partial Differential Equations
Front Matter....Pages i-ix
Introduction....Pages 1-17
Front Matter....Pages 19-19
A Framework for Function Spaces....Pages 21-68
Variable Exponent Lebesgue Spaces....Pages 69-97
The Maximal Operator....Pages 99-141
The Generalized Muckenhoupt Condition * ....Pages 143-197
Classical Operators....Pages 199-212
Transfer Techniques....Pages 213-244
Front Matter....Pages 245-245
Introduction to Sobolev Spaces....Pages 247-288
Density of Regular Functions....Pages 289-314
Capacities....Pages 315-338
Fine Properties of Sobolev Functions....Pages 339-366
Other Spaces of Differentiable Functions....Pages 367-398
Front Matter....Pages 399-399
Dirichlet Energy Integral and Laplace Equation....Pages 401-436
PDEs and Fluid Dynamics....Pages 437-481
Back Matter....Pages 483-509
