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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Sobolev versus Holder local minimizers in degenerate Kirchhoff type problems

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Iturriaga, Leonelo [1] ; Massa, Eugenio [2]
Total Authors: 2
[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
Total Affiliations: 2
Document type: Journal article
Source: Journal of Differential Equations; v. 269, n. 5, p. 4381-4405, AUG 15 2020.
Web of Science Citations: 0

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)

FAPESP's process: 19/19699-0 - Concave-convex type problems with local and nonlocal operators
Grantee:Eugenio Tommaso Massa
Support type: Scholarships abroad - Research
FAPESP's process: 14/25398-0 - Elliptic equations and systems with several kinds of interaction with the spectrum
Grantee:Eugenio Tommaso Massa
Support type: Regular Research Grants