Overdetermined elliptic problems in onduloid-type domains with general nonlinearities

Ruiz Aguilar, David; Sicbaldi, Pieralberto; Wu, Jing

doi:10.1016/j.jfa.2022.109705

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Identificadores

URI: https://hdl.handle.net/10481/77400

DOI: 10.1016/j.jfa.2022.109705

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Editorial

Elsevier

Materia

Overdetermined boundary conditions

Semilinear elliptic problems

Bifurcation theory

Fecha

2021-07-23

Referencia bibliográfica

Published version: David Ruiz, Pieralberto Sicbaldi, Jing Wu, Overdetermined elliptic problems in onduloid-type domains with general nonlinearities, Journal of Functional Analysis, Volume 283, Issue 12, 2022, 109705, ISSN 0022-1236, [https://doi.org/10.1016/j.jfa.2022.109705]

Patrocinador

Spanish Government MTM2017-89677-P FQM-116; China Scholarship Council CSC201906290013; Ministry of Science and Innovation, Spain (MICINN) PGC2018-096422-B-I00; J. Andalucia CEX2020-001105-M P18-FR-4049 A-FQM-139-UGR18

Resumen

In this paper, we prove the existence of nontrivial unbounded domains omega subset of Rn+1, n >= 1, bifurcating from the straight cylinder BxR (where B is the unit ball of R-n), such that the overdetermined elliptic problem {delta u + f(u) = 0 in omega, u = 0 on & part;omega, & part;(nu)u = constant on & part;omega, has a positive bounded solution. We will prove such result for a very general class of functions f: [0, + infinity) -> 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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