Lebesgue and Sobolev Spaces with Variable Exponents

• Main Authors: Diening, Lars (Author), Harjulehto, Petteri (Author), Hästö, Peter (Author), Ruzicka, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Lecture Notes in Mathematics, 2017
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Partial differential equations.; Analysis.; Functional Analysis.; Partial Differential Equations.

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 ti...

Table of Contents:

• 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.