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Displaying 21 – 33 of 33

On the definition and properties of p-superharmonic functions.

Peter Lindqvist (1986)

Journal für die reine und angewandte Mathematik

On the Dirichlet problem associated with the Dunkl Laplacian

Mohamed Ben Chrouda (2016)

Annales Polonici Mathematici

This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian $Δ_{k}$ as well as the hypoellipticity of $Δ_{k}$ on noninvariant open sets.

On the Dirichlet problem for functions of the first Baire class

Jiří Spurný (2001)

Commentationes Mathematicae Universitatis Carolinae

Let $ℋ$ be a simplicial function space on a metric compact space $X$ . Then the Choquet boundary $Ch X$ of $ℋ$ is an $F_{σ}$ -set if and only if given any bounded Baire-one function $f$ on $Ch X$ there is an $ℋ$ -affine bounded Baire-one function $h$ on $X$ such that $h = f$ on $Ch X$ . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set $X$ .

On the Harmonie Continuation of Bounded Harmonie Functions.

Jaakko Hyvönen (1979)

Mathematische Annalen

On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^{n} \times ℝ^{m}$ , m ≥ 2

Ewa Ligocka (1999)

Annales Polonici Mathematici

We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.

On the mean value property of superharmonic and subharmonic functions.

Dalmasso, Robert (2006)

International Journal of Mathematics and Mathematical Sciences

On the mean-value property of superharmonic functions

Robert Dalmasso (2008)

Annales Polonici Mathematici

We complement a previous result concerning a converse of the mean-value property for smooth superharmonic functions. The case of harmonic functions was treated by Kuran and an improvement was given by Armitage and Goldstein.

On the potential theory of some systems of coupled PDEs

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri, Sabah Haddad (2016)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_{1} u = - μ_{1} v$ , $L_{2} v = - μ_{2} u$ , on a domain $D$ of $ℝ^{d}$ , where $μ_{1}$ and $μ_{2}$ are suitable measures on $D$ , and $L_{1}$ , $L_{2}$ are two second order linear differential elliptic operators on $D$ with coefficients of class $𝒞^{\infty}$ . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with $L_{1}$ and $L_{2}$ , and a convergence...

Displaying 21 – 33 of 33

On the definition and properties of p-superharmonic functions.

On the Dirichlet problem associated with the Dunkl Laplacian

On the Dirichlet problem for functions of the first Baire class

On the Harmonie Continuation of Bounded Harmonie Functions.

On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^{n} \times ℝ^{m}$ , m ≥ 2

On the mean value property of superharmonic and subharmonic functions.

On the mean-value property of superharmonic functions

On the potential theory of some systems of coupled PDEs

On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in $R^{n}$

On the space and dual space of functions representable by differences of subharmonic functions

On the space of Bloch harmonic functions and interpolation of spaces of harmonic and holomorphic functions

On Veech's conjecture for harmonic functions

On weighed $H^{p}$ spaces

Currently displaying 21 – 33 of 33