Overdetermined elliptic problems in onduloid-type domains with general nonlinearities

In this paper, we prove the existence of nontrivial unbounded domains Ω⊂Rn+1,n≥1, bifurcating from the straight cylinder B×R (where B is the unit ball of Rn), such that the overdetermined elliptic problem{Δu+f(u)=0in Ω, u=0on ∂Ω, ∂νu=constanton ∂Ω, has a positive bounded solution. We will prove suc...

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Vydané v:	Journal of functional analysis Ročník 283; číslo 12; s. 109705
Hlavní autori:	Ruiz, David, Sicbaldi, Pieralberto, Wu, Jing
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 15.12.2022
Predmet:	Bifurcation theory Overdetermined boundary conditions Semilinear elliptic problems Semilinear elliptic problems Bifurcation theory Overdetermined boundary conditions 35J61 35N15
ISSN:	0022-1236, 1096-0783
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Popis
Shrnutí:	In this paper, we prove the existence of nontrivial unbounded domains Ω⊂Rn+1,n≥1, bifurcating from the straight cylinder B×R (where B is the unit ball of Rn), such that the overdetermined elliptic problem{Δu+f(u)=0in Ω, u=0on ∂Ω, ∂νu=constanton ∂Ω, has a positive bounded solution. We will prove such result for a very general class of functions f:[0,+∞)→R. Roughly speaking, we only ask that the Dirichlet problem in B admits a nondegenerate solution. The proof uses a local bifurcation argument.
ISSN:	0022-1236 1096-0783
DOI:	10.1016/j.jfa.2022.109705