#potential-theory

31. Potential Theory

This volume studies harmonic, subharmonic, and superharmonic functions, along with potentials and their applications to analysis, geometry, and physics. It connects closely with partial differential equations and complex analysis. Part I. Foundations Chapter 1. Harmonic Functions 1.1 Definition via Laplace equation 1.2 Mean value property 1.3 Maximum and minimum principles 1.4 Uniqueness results 1.5 Examples Chapter 2. Subharmonic and Superharmonic Functions 2.1 Definitions 2.2 Basic properties 2.3 Comparison principles 2.4...