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.;
2008-01-01
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
JDE(2008).pdf
Solo gestori archvio
Descrizione: articolo principale
Tipologia:
Versione Editoriale
Dimensione
351.28 kB
Formato
Adobe PDF
|
351.28 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
