Infinite dimension of solutions of the Dirichlet problem

Vladimir Ryazanov

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The Dirichlet problem with non-compact boundary.

Stephen J. Gardiner (1993)

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On the boundary values of harmonic functions.

Paul R. Garabedian (1985)

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Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the...

The product of two Dirichlet series

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Dirichlet problem with L $^{p}$ -boundary data in contractible domains of Carnot groups

Andrea Bonfiglioli, Ermanno Lanconelli (2006)

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Let $ℒ$ be a sub-laplacian on a stratified Lie group $G$ . In this paper we study the Dirichlet problem for $ℒ$ with $L^{p}$ -boundary data, on domains $Ω$ which are contractible with respect to the natural dilations of $G$ . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for $ℒ$ . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.

A Maximum Principle for Harmonic Mappings Which Solve A Dirichlet Problem.

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Harmonic majorization of $| x_{1} |$ in subsets of $ℝ^{n}$ , $n \geq 2$ .

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Dirichlet Problem for n-Harmonic Functions and Related Geometrical Properties.

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Generalized multiple Dirichlet series and generalized multiple polylogarithms

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A. Mallik (1981)

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Growth of coefficients of universal Dirichlet series

A. Mouze (2007)

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We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.

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.