Measure Theory and Nonlinear Evolution Equations

✍ Scribed by Flavia Smarrazzo; Alberto Tesei

• Publisher: De Gruyter
• Year: 2022
• Tongue: English
• Leaves: 456
• Series: De Gruyter Studies in Mathematics; 86
• Category: Library

✦ Synopsis

This text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity. A comprehensive discussion of applications to quasilinear parabolic and hyperbolic problems is provided.

• Presents basic and advanced measure theory with a view toward PDE's
• Covers Radon and Young measures, capacity, vector-valued functions, weak convergence, etc.
• Of interest to graduate students and researchers working in the analysis of PDE's

✦ Table of Contents

Contents
Preface
Introduction
Part I: General theory
Outline of Part I
1 Measure theory
2 Scalar integration and differentiation
3 Function spaces and capacity
4 Vector integration
5 Sequences of finite Radon measures
Part II: Applications
Outline of Part II
6 Case study 1: quasilinear parabolic equations
7 Case study 2: hyperbolic conservation laws
8 Case study 3: forward–backward parabolic equations
Bibliography
Appendix A Topological spaces
List of Symbols
Index