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Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains

Mohamed Amine Ben BoubakerMohamed Selmi — 2013

Colloquium Mathematicae

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.

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