On the stability of the Serrin problem |
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| Authors: | B. Brandolini |
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| Affiliation: | a Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy
b Dipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy |
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| Abstract: | We investigate stability issues concerning the radial symmetry of solutions to Serrin's overdetermined problems. In particular, we show that, if u is a solution to Δu=n in a smooth domain Ω⊂Rn, u=0 on ∂Ω and |Du| is “close” to 1 on ∂Ω, then Ω is “close” to the union of a certain number of disjoint unitary balls. |
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| Keywords: | 35B05 35B35 35J05 |
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