Symmetry problems for elliptic systems

Robert Dalmasso (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

We consider overdetermined boundary value problems for elliptic systems. Using the maximum principle and the techniques of moving up planes perpendicular to a fixed direction we show that if a solution exists, then the domain must be a ball and the solution radially symmetric.

Mots clés: elliptic systems; maximum principle

Domaines: Equations aux dérivées partielles [math.AP]

Robert Dalmasso. Symmetry problems for elliptic systems. Hokkaido Mathematical Journal, 1996, 25 (1), pp.107-117. ⟨10.14492/hokmj/1351516712⟩. ⟨hal-00387653⟩