Smarrazzo F. Measure Theory and Nonlinear Evolution Equat. 2022

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Теория меры и нелинейные эволюционные уравнения
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.
General theory
Measure theory
Scalar integration and differentiation
Function spaces and capacity
Vector integration
Sequences of finite Radon measures
Applications
Case study 1: quasilinear parabolic equations
Case study 2: hyperbolic conservation laws
Case study 3: forward–backward parabolic equations
Appendix A Topological spaces