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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| Vydáno v: | Journal of functional analysis Ročník 283; číslo 12; s. 109705 |
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15.12.2022
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 109705 |
| Author | Ruiz, David Wu, Jing Sicbaldi, Pieralberto |
| Author_xml | – sequence: 1 givenname: David orcidid: 0000-0001-9837-3101 surname: Ruiz fullname: Ruiz, David email: daruiz@ugr.es organization: Departamento de Análisis matemático, Universidad de Granada, Campus Fuentenueva, 18071 Granada, Spain – sequence: 2 givenname: Pieralberto surname: Sicbaldi fullname: Sicbaldi, Pieralberto email: pieralberto@ugr.es organization: Departamento de Análisis matemático, Universidad de Granada, Campus Fuentenueva, 18071 Granada, Spain – sequence: 3 givenname: Jing surname: Wu fullname: Wu, Jing email: jingwulx@correo.ugr.es organization: Departamento de Análisis matemático, Universidad de Granada, Campus Fuentenueva, 18071 Granada, Spain |
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| Cites_doi | 10.1007/s00526-009-0264-z 10.1002/cpa.21696 10.4171/jems/921 10.1016/j.jfa.2013.09.012 10.1016/j.aim.2011.10.001 10.1007/BF03321614 10.1007/s002050050034 10.1007/s00039-014-0268-5 10.1007/s00205-016-1044-5 10.1016/j.jde.2013.04.027 10.1007/BF00250468 10.1051/cocv/2014064 10.1007/BF00251502 10.1215/00127094-3146710 10.1016/0022-1236(71)90015-2 10.36045/bbms/1203692453 10.1007/s002050050103 10.1002/(SICI)1097-0312(199711)50:11<1089::AID-CPA2>3.0.CO;2-6 10.1007/BF01221125 10.1007/s00205-009-0227-8 |
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