Sobolev versus Holder local minimizers in degenerate Kirchhoff type problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Iturriaga, Leonelo¹  Massa, Eugenio² 

[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

关键词: Nonlocal elliptic problems;    Kirchhoff equation;    Degenerate problems;    Variational methods;    Critical point theory;    Local minimizers;   

DOI  :  10.1016/j.jde.2020.03.031

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free