Quasi-Balayage and a Priori Estimates for the Laplace Operator

摘要

The notion of balayage, as embodied in Proposition 2.1, is very important inpotential theory. In the present paper the authors present a generalization, called quasi-balayage; while formally this is straightforward, and perhaps not of great intrinsic interest, it enables one to prove new a priori estimates for the Laplace operator, and also to derive some known ones in a novel and simple manner.