Geodesic
Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains
Mohamed Amine Ben Boubaker 1   ; Mohamed Selmi 2
1 Institut Preparatoire aux Études d'Ingénieur de Nabeul Université de Carthage Campus Universitaire Merezka 8000, Nabeul, Tunisia
2 Faculty of Sciences of Tunis Department of Mathematics University of Tunis el Manar Campus Universitaire 2092, Tunis, Tunisia
Colloquium Mathematicum, Tome 133 (2013) no. 1, pp. 1-22 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm133-1-1
Keywords: establish inequalities green functions general bounded piecewise dini smooth jordan domains mathbb enables prove version theorem which generalizes its previous version given nbsp selmi potential anal using these results comparison theorem green kernel delta green kernel delta where nonnegative exact radon measure

Mohamed Amine Ben Boubaker  1   ; Mohamed Selmi  2

1 Institut Preparatoire aux Études d'Ingénieur de Nabeul Université de Carthage Campus Universitaire Merezka 8000, Nabeul, Tunisia
2 Faculty of Sciences of Tunis Department of Mathematics University of Tunis el Manar Campus Universitaire 2092, Tunis, Tunisia 
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Mohamed Amine Ben Boubaker; Mohamed Selmi. Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains. Colloquium Mathematicum, Tome 133 (2013) no. 1, pp. 1-22. doi: 10.4064/cm133-1-1

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