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Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.

Ren, Guangbin, Malonek, Helmuth R. (2010)

Journal of Inequalities and Applications [electronic only]

Deformation from symmetry for Schrödinger equations of higher order on unbounded domains.

Salvatore, Addolorata, Squassina, Marco (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Densité de l'intégrale d'aire dans Rn+ +1 et limites non tangentielles.

Jean Brossard (1988)

Inventiones mathematicae

Determination of the pluripolar hull of graphs of certain holomorphic functions

Armen Edigarian, Jan Wiegerinck (2004)

Annales de l’institut Fourier

Let $A$ be a closed polar subset of a domain $D$ in $ℂ$ . We give a complete description of the pluripolar hull $Γ_{D \times ℂ}^{*}$ of the graph $Γ$ of a holomorphic function defined on $D ∖ A$ . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

Deux généralisation du «théorèm des trois cercles» de Hadamard.

Michel Lassalle (1980)

Mathematische Annalen

Développements en séries trigonométriques de certaines fonctions périodiques vérifiant l’équation $Δ F = o$

Appell (1887)

Journal de Mathématiques Pures et Appliquées

Dichotomy of global density of Riesz capacity

Hiroaki Aikawa (2016)

Studia Mathematica

Let $C_{α}$ be the Riesz capacity of order α, 0 < α < n, in ℝⁿ. We consider the Riesz capacity density $̲ (C_{α}, E, r) = i n f_{x \in ℝ ⁿ} C_{α} (E \cap B (x, r)) / C_{α} (B (x, r))$ for a Borel set E ⊂ ℝⁿ, where B(x,r) stands for the open ball with center at x and radius r. In case 0 < α ≤ 2, we show that $l i m_{r \to \infty} ̲ (C_{α}, E, r)$ is either 0 or 1; the first case occurs if and only if $̲ (C_{α}, E, r)$ is identically zero for all r > 0. Moreover, it is shown that the densities with respect to more general open sets enjoy the same dichotomy. A decay estimate for α-capacitary potentials is also obtained.

Die Existenz einer Greenschen Funktion auf Riemannschen Mannigfaltigkeiten

Sebastian Keller (1973)

Commentarii mathematici Helvetici

Différentiabilité des fonctions finement harmoniques.

A. Debiard, B. Gaveau (1975)

Inventiones mathematicae

Différentiabilité fine et capacités

Michèle Mastrangelo, Danièle Dehen (1982)

Bulletin de la Société Mathématique de France

Différentiabilité fine et différentiabilité sur des compacts

Michèle Mastrangelo (1980)

Bulletin de la Société Mathématique de France

Dirchlet's problem on Green lines and some convergence theorems for Denjoy's domains.

J. Salazar (1993)

Mathematische Zeitschrift

Dirichlet finite biharmonic functions on the Poincaré N-ball.

L. Sario, C. Wang, D. Hada (1975)

Journal für die reine und angewandte Mathematik

Dirichlet Finite Biharmonic Functions with Dirichlet Finite Laplacians.

Mitsuru Nakai, Leo Sario (1971)

Mathematische Zeitschrift

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

Andrea Bonfiglioli, Ermanno Lanconelli (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

Dispersion relations for the multivelocity acoustic Peierls equations and some properties of the scalar acoustic Peierls potential. I, II.

Kirejtov, V.R. (2001)

Sibirskij Matematicheskij Zhurnal

Distribution function inequalities for the area integral

D. Burkholder, R. Gundy (1972)