A local symmetry result for linear elliptic problems with solutions changing sign
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 4, p. 551-564

We prove that the only domain Ω such that there exists a solution to the following problem Δu+ω 2 u=-1 in Ω, u=0 on ∂Ω, and 1 |Ω| Ω 𝐧 u=c, for a given constant c, is the unit ball B 1 , if we assume that Ω lies in an appropriate class of Lipschitz domains.

@article{AIHPC_2011__28_4_551_0,
     author = {Canuto, B.},
     title = {A local symmetry result for linear elliptic problems with solutions changing sign},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {4},
     year = {2011},
     pages = {551-564},
     doi = {10.1016/j.anihpc.2011.03.005},
     zbl = {1242.35182},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_4_551_0}
}
Canuto, B. A local symmetry result for linear elliptic problems with solutions changing sign. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 4, pp. 551-564. doi : 10.1016/j.anihpc.2011.03.005. http://www.numdam.org/item/AIHPC_2011__28_4_551_0/

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