A RIGIDITY RESULT FOR OVERDETERMINED ELLIPTIC PROBLEMS IN THE PLANE
Résumé
Let f : [0, +∞) → R be a (locally) Lipschitz function and Ω ⊂ R 2 a C 1,α domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined elliptic problem ∆u + f (u) = 0 in Ω u = 0 on ∂Ω ∂u ∂ ν = 1 on ∂Ω we prove that Ω is a half-plane. In particular, we obtain a partial answer to a question raised by H. Berestycki, L. Caffarelli and L. Nirenberg in 1997.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...