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...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of functional analysis Vol. 283; no. 12; p. 109705
Main Authors:	Ruiz, David, Sicbaldi, Pieralberto, Wu, Jing
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.12.2022
Subjects:	Bifurcation theory Overdetermined boundary conditions Semilinear elliptic problems Semilinear elliptic problems Bifurcation theory Overdetermined boundary conditions 35J61 35N15
ISSN:	0022-1236, 1096-0783
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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