An overdetermined problem for harmonic functions

Robert Dalmasso (1)

1 EDP - Equations aux Dérivées Partielles

Let Ω⊂Rn be a bounded connected open set with connected real analytic boundary. We show that, if there exist n harmonic functions satisfying some appropriate boundary conditions, then Ω is a ball.

Mots clés: Overdetermined problem; Harmonic functions

Domaines: Equations aux dérivées partielles [math.AP]

Robert Dalmasso. An overdetermined problem for harmonic functions. Journal of Mathematical Analysis and Applications, 2012, 385 (2), pp.1044-1054. ⟨10.1016/j.jmaa.2011.07.030⟩. ⟨hal-00666489⟩