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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Veröffentlicht in:Journal of functional analysis Jg. 283; H. 12; S. 109705
Hauptverfasser: Ruiz, David, Sicbaldi, Pieralberto, Wu, Jing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.12.2022
Schlagworte:
Bifurcation theory
Overdetermined boundary conditions
Semilinear elliptic problems
Semilinear elliptic problems
Bifurcation theory
Overdetermined boundary conditions
35J61
35N15
ISSN:0022-1236, 1096-0783
Online-Zugang:Volltext
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Zusammenfassung: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