Mathematics – Functional Analysis
Scientific paper
2008-11-10
Mathematics
Functional Analysis
v3: 25 pages, heavily revised background theory in early sections. v2: 30 pages; added 2 sections, complete revision of proofs
Scientific paper
In this paper we explore two constructions of the same family of metric measure spaces. The first construction was introduced by Laakso in 2000 where he used it as an example that Poincar\'e inequalities can hold on spaces of arbitrary Hausdorff dimension. This was proved using minimal generalized upper gradients. Following Cheeger's work these upper gradients can be used to define a Sobolev space. We show that this leads to a Dirichlet form. The second construction was introduced by Barlow and Evans in 2004 as a way of producing exotic spaces along with Markov processes from simpler spaces and processes. We show that for the correct base process in the Barlow Evans construction that this Markov process corresponds to the Dirichlet form derived from the minimal generalized upper gradients.
No associations
LandOfFree
Dirichlet Forms on Laakso and Barlow-Evans Fractals of Arbitrary Dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dirichlet Forms on Laakso and Barlow-Evans Fractals of Arbitrary Dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirichlet Forms on Laakso and Barlow-Evans Fractals of Arbitrary Dimension will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-724455