A note on some overdetermined elliptic problem - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2010

A note on some overdetermined elliptic problem

Résumé

We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the boundary. We study the two-dimensional case: we present various examples and give a general construction algorithm of such surface by using complex analysis. We deduce a classification of all such surfaces assuming some further natural hypotheses and prove a Bernstein type theorem.
Fichier principal
Vignette du fichier
2010-01-05-harmonic-overdetermined-problem.pdf (183.72 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00444828 , version 1 (07-01-2010)

Identifiants

Citer

Frédéric Hélein, Laurent Hauswirth, Frank Pacard. A note on some overdetermined elliptic problem. 2010. ⟨hal-00444828⟩
173 Consultations
137 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More