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, 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.
On the stability of the Serrin problem / B. Brandolini; C. Nitsch; P. Salani; C. Trombetti. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 245 n.6:(2008), pp. 1566-1583. [10.1016/j.jde.2008.06.010]
On the stability of the Serrin problem
SALANI, PAOLO;
2008
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, 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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