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Théorie du potentiel et domaines de John

Alano Ancona

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Abstract

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.

Article information

Source
Publ. Mat., Volume 51, Number 2 (2007), 345-396.

Dates
First available in Project Euclid: 31 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.pm/1185912167

Mathematical Reviews number (MathSciNet)
MR2334795

Zentralblatt MATH identifier
1134.31009

Subjects
Primary: 31C15: Potentials and capacities 31C25: Dirichlet spaces 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

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

Citation

Ancona, Alano. Théorie du potentiel et domaines de John. Publ. Mat. 51 (2007), no. 2, 345--396. https://projecteuclid.org/euclid.pm/1185912167


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References

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