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Displaying 61 – 80 of 251

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.

Discrete groups and thin sets.

Lundh, Torbjörn (1998)

Annales Academiae Scientiarum Fennicae. Mathematica

Distribution function inequalities for the area integral

D. Burkholder, R. Gundy (1972)

Studia Mathematica

Distributions bi-sousharmoniques sur $𝐑^{n} (n \geq 2)$

Allami Benyaiche (1994)

Mathematica Bohemica

L’object de ce travail est l’etude des fonctions fonctions localement sommable $ω$ sur $𝐑^{n}, n \geq 2$ , vérifiant $Δ^{2} ω \geq 0$ (où $Δ$ est Laplacien pris au sens des distributions) et que se comportent à l’infini comme des fonctions sousharmoniques. En parculier, nous caractérisons les fonctious qui sont à la fois bi-sousharmoniques et sousharmoniques.

Doubling conditions for harmonic measure in John domains

Hiroaki Aikawa, Kentaro Hirata (2008)

Annales de l’institut Fourier

We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain $D$ satisfies certain doubling conditions if and only if $D$ is a semi-uniform domain or an inner semi-uniform domain.

Eigenvalue Inequalities for the Dirichlet Problem on Spheres and the Growth of Subharmonic Functions

W.K. Hayman, S. Friedland (1976)

Commentarii mathematici Helvetici

El espacio de Montel de las funciones vectoriales armónicas en un dominio.

Gonzalo González De Buitrago Díaz (1977)

Gaceta Matemática

Elementary proofs of some basic subtemperature theorems

Neil A. Watson (2002)

Colloquium Mathematicae

We present simple elementary proofs of several theorems about temperatures and subtemperatures. Most of these are concerned with mean values over heat spheres, heat balls, and modified heat balls, with applications to proving Harnack theorems and the monotone approximation of subtemperatures by smooth subtemperatures.

Embedding of open riemannian manifolds by harmonic functions

Robert E. Greene, H. Wu (1975)

Annales de l'institut Fourier

Let $M$ be a noncompact Riemannian manifold of dimension $n$ . Then there exists a proper embedding of $M$ into $R^{2 n + 1}$ by harmonic functions on $M$ . It is easy to find $2 n + 1$ harmonic functions which give an embedding. However, it is more difficult to achieve properness. The proof depends on the theorems of Lax-Malgrange and Aronszajn-Cordes in the theory of elliptic equations.

Energy and the law of the interated logarithm.

J.R. Baxter, G.A. Brosamler (1976)

Mathematica Scandinavica

Equivalence of weak and viscosity solutions to the $p$ -Laplace equation in the Heisenberg group.

Bieske, Thomas (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

Equivalent Norms on L... Spaces of Harmonic Functions.

Daniel H. Luecking (1983)

Monatshefte für Mathematik

Espaces harmoniques sans potentiel positif

Victor Anandam (1972)

Annales de l'institut Fourier

Dans cet article on étudie les fonctions surharmoniques dans un espace $Ω$ muni de la théorie axiomatique des fonctions harmoniques avec les axiomes 1, 2, 3 de M. Brelot, en supposant que les constantes sont harmoniques dans $Ω$ et qu’il n’existe pas de potentiel $> 0$ dans $Ω$ . Ainsi, dans la théorie axiomatique, on se propose de chercher à étendre les particularités du cas plan et quelques résultats sur les surfaces de Riemann du type parabolique. On démontre premièrement, en utilisant une notion de flux...

Estimate for gradient, bmo and Lindelöf theorem

M. Mateljević (1995)

Publications de l'Institut Mathématique

Estimates for the Poisson kernel on higher rank NA groups

Richard Penney, Roman Urban (2010)