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 Δ u = n in a smooth domain Ω ⊂ Rn, u = 0 on ∂Ω and | D u | is "close" to 1 on ∂Ω, then Ω is "close" to the union of a certain number of disjoint unitary balls.

Brandolini B., Nitsch C., Salani P., & Trombetti C. (2008). On the stability of the Serrin problem. JOURNAL OF DIFFERENTIAL EQUATIONS, 245(6), 1566-1583 [10.1016/j.jde.2008.06.010].

On the stability of the Serrin problem

Brandolini B.;
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 Δ u = n in a smooth domain Ω ⊂ Rn, u = 0 on ∂Ω and | D u | is "close" to 1 on ∂Ω, then Ω is "close" to the union of a certain number of disjoint unitary balls.
Settore MAT/05 - Analisi Matematica
Brandolini B., Nitsch C., Salani P., & Trombetti C. (2008). On the stability of the Serrin problem. JOURNAL OF DIFFERENTIAL EQUATIONS, 245(6), 1566-1583 [10.1016/j.jde.2008.06.010].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494034
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