Sobolev versus Holder local minimizers in degenerate Kirchhoff type problems

Autor(es)

Iturriaga, Leonelo ^[1] ; Massa, Eugenio ^[2]

Afiliação do(s) autor(es)

^[1] Univ Tecn Federico Santa Maria, Dept Matemat, Ave Espana 1680, Casilla 110-5, Valparaiso - Chile

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 269, n. 5, p. 4381-4405, AUG 15 2020.
• Citações Web of Science: 0

Resumo

In this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of Kirchhoff type. Due to the degeneration of the nonlocal term it is not possible to directly use classical results such as uniform a-priori estimates and ``Sobolev versus Holder local minimizers{''} type of results. We prove that results similar to these hold true or not, depending on how degenerate the problem is. We apply our findings in order to show existence and multiplicity of solutions for the associated quasilinear equations, considering several different interactions between the nonlocal term and the nonlinearity. (c) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 19/19699-0 - Problemas de tipo côncavo-convexo, com operadores locais e não locais
• Beneficiário: Eugenio Tommaso Massa
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 14/25398-0 - Equações e sistemas elípticos com vários tipos de interação com o espectro
• Beneficiário: Eugenio Tommaso Massa
• Modalidade de apoio: Auxílio à Pesquisa - Regular