A local symmetry result for linear elliptic problems with solutions changing sign

Canuto, B.

doi:10.1016/j.anihpc.2011.03.005

Canuto, B.

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 551-564

Résumé

We prove that the only domain Ω such that there exists a solution to the following problem $Δ u + ω^{2} u = - 1$ in Ω, $u = 0$ on ∂Ω, and $\frac{1}{| \partial Ω |} \int_{\partial Ω} \partial_{𝐧} u = c$ , for a given constant c, is the unit ball $B_{1}$ , if we assume that Ω lies in an appropriate class of Lipschitz domains.

Zbl

DOI : 10.1016/j.anihpc.2011.03.005

@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},
     pages = {551--564},
     year = {2011},
     publisher = {Elsevier},
     volume = {28},
     number = {4},
     doi = {10.1016/j.anihpc.2011.03.005},
     zbl = {1242.35182},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2011.03.005/}
}

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Canuto, B. A local symmetry result for linear elliptic problems with solutions changing sign. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 551-564. doi: 10.1016/j.anihpc.2011.03.005

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