Boundary multifractal behaviour for harmonic functions in the ball - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Potential Analysis Année : 2013

Boundary multifractal behaviour for harmonic functions in the ball

Résumé

It is well known that if $h$ is a nonnegative harmonic function in the ball of $\RR^{d+1}$ or if $h$ is harmonic in the ball with integrable boundary values, then the radial limit of $h$ exists at almost every point of the boundary. In this paper, we are interested in the exceptional set of points of divergence and in the speed of divergence at these points. In particular, we prove that for generic harmonic functions and for any $\beta\in [0,d]$, the Hausdorff dimension of the set of points $\xi$ on the sphere such that $h(r\xi)$ looks like $(1-r)^{-\beta}$ is equal to $d-\beta$.
Fichier principal
Vignette du fichier
multifpoisson7.pdf (146.06 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00635997 , version 1 (26-10-2011)
hal-00635997 , version 2 (22-03-2012)

Identifiants

Citer

Frédéric Bayart, Yanick Heurteaux. Boundary multifractal behaviour for harmonic functions in the ball. Potential Analysis, 2013, 38 (2), pp.499-514. ⟨hal-00635997v2⟩
83 Consultations
132 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More