Lebesgue and Sobolev Spaces with Variable Exponents [electronic resource] / by Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Ruzicka.
By: Diening, Lars [author.].
Contributor(s): Harjulehto, Petteri [author.] | Hästö, Peter [author.] | Ruzicka, Michael [author.] | SpringerLink (Online service).
Material type:
BookSeries: Lecture Notes in Mathematics: 2017Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: IX, 509p. 10 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642183638.Subject(s): Mathematics | Global analysis (Mathematics) | Functional analysis | Differential equations, partial | Mathematics | Analysis | Functional Analysis | Partial Differential EquationsDDC classification: 515 Online resources: Click here to access online 1 Introduction -- 2 A framework for function spaces -- 3 Variable exponent Lebesgue spaces -- 4 The maximal operator -- 5 The generalized Muckenhoupt condition* -- 6 Classical operators -- 7 Transfer techniques -- 8 Introduction to Sobolev spaces -- 9. Density of regular functions -- 10. Capacities -- 11 Fine properties of Sobolev functions -- 12 Other spaces of differentiable functions -- 13 Dirichlet energy integral and Laplace equation -- 14 PDEs and fluid dynamics.
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.
There are no comments for this item.