Displaying similar documents to “Harmonic Spaces Associated with Non-Symmetric Translation Invariant Dirichlet Forms.”

Infinite dimension of solutions of the Dirichlet problem

Vladimir Ryazanov (2015)

Open Mathematics

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It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals

Jiaxin Hu, Xingsheng Wang (2006)

Studia Mathematica

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We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.