We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in ℝ². 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 Δ and the Green kernel of Δ - μ, where μ is a nonnegative and exact Radon measure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-1,
author = {Mohamed Amine Ben Boubaker and Mohamed Selmi},
title = {Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {1-22},
zbl = {1283.81071},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-1}
}
Mohamed Amine Ben Boubaker; Mohamed Selmi. Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains. Colloquium Mathematicae, Tome 131 (2013) pp. 1-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-1/