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2007 Théorie du potentiel et domaines de John
Alano Ancona
Publ. Mat. 51(2): 345-396 (2007).


Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.


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Alano Ancona. "Théorie du potentiel et domaines de John." Publ. Mat. 51 (2) 345 - 396, 2007.


Published: 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1134.31009
MathSciNet: MR2334795

Primary: 31C15 , 31C25 , 35J05 , 46E35

Keywords: Green's function , Harnack boundary principle , John domain , Martin boundary , Naïm kernel , quasi-metric , radial limit theorem

Rights: Copyright © 2007 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.51 • No. 2 • 2007
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