The 3G inequality for a uniformly John domain
Let G be the Green function for a domain D Rd with d ≥ 3. The Martin boundary of D and the 3G inequality:
for x,y,z 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.
Permanent link to this document: http://projecteuclid.org/euclid.kmj/1123767003
Digital Object Identifier: doi:10.2996/kmj/1123767003
Zentralblatt MATH identifier: 1079.31002
Mathematical Reviews number (MathSciNet): MR2153910