Balayage Theory

Abstract

The content of this chapter is the main issue of the book. Almost all principal results in potential theory depend on properties of the reduit and its regularization, the balayage. Therefore the study of the functions

$${\text{R:}}\left( {{\text{u}},{\text{A,x}}} \right) \mapsto R_{\text{u}}^{\text{A}} \left( {\text{x}} \right){\text{and}}\hat R:\left( {{\text{u}},{\text{A,x}}} \right) \mapsto \hat R_{\text{u}}^{\text{A}} \left( {\text{x}} \right)$$

is the most important tool.