The 3G inequality for a uniformly John domain
Artikel i vetenskaplig tidskrift, 2005

Let G be the Green function for a domain D $\subset$ Rd with d ≥ 3. The Martin boundary of D and the 3G inequality: $\frac{G(x,y)G(y,z)}{G(x,z)} \le A(|x-y|^{2-d}+|y-z|^{2-d})$ for x,y,z $\in$ D are studied. We give the 3G inequality for a bounded uniformly John domain D, although the Martin boundary of D need not coincide with the Euclidean boundary. On the other hand, we construct a bounded domain such that the Martin boundary coincides with the Euclidean boundary and yet the 3G inequality does not hold.

3G inequality

Green function

inner uniform domain

uniformly Johyan domain

boundary Harnack principle


Torbjörn Lundh

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Kodai Mathematical Journal

Vol. 28 209-219


Matematisk analys