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

Volume 133 / 2013

Mohamed Amine Ben Boubaker, Mohamed Selmi 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.

Authors

  • Mohamed Amine Ben BoubakerInstitut Preparatoire aux Études d'Ingénieur de Nabeul
    Université de Carthage
    Campus Universitaire Merezka
    8000, Nabeul, Tunisia
    e-mail
  • Mohamed SelmiFaculty of Sciences of Tunis
    Department of Mathematics
    University of Tunis el Manar
    Campus Universitaire
    2092, Tunis, Tunisia
    e-mail

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