Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 1-22
MSC: Primary 81Q15; Secondary 31A35, 30C35.
DOI: 10.4064/cm133-1-1
Abstract
We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in $\mathbb {R}^2$. This enables us to prove a new version of the 3G Theorem which generalizes its previous version given in [M. Selmi, Potential Anal. 13 (2000)]. Using these results, we give a comparison theorem for the Green kernel of $\Delta $ and the Green kernel of $\Delta -\mu $, where $\mu $ is a nonnegative and exact Radon measure.
