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Revista Matemática Iberoamericana

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Volume 34, Issue 1, 2018, pp. 195–220
DOI: 10.4171/RMI/983

Published online: 2018-02-06

A priori bounds and existence of solutions for some nonlocal elliptic problems

Begoña Barrios[1], Leandro M. Del Pezzo[2], Jorge García-Melián[3] and Alexander Quaas[4]

(1) University of Texas at Austin, USA
(2) CONICET and Universidad de Buenos Aires, Argentina
(3) Universidad de La Laguna, Tenerife, Spain
(4) Universidad Técnica Federico Santa María, Valparaíso, Chile

In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We obtain the a priori bounds by adapting the classical scaling method of Gidas and Spruck. We also deal with problems involving gradient terms.

Keywords: Nonlocal diffusion problems, a priori estimates, topological degree

Barrios Begoña, Del Pezzo Leandro, García-Melián Jorge, Quaas Alexander: A priori bounds and existence of solutions for some nonlocal elliptic problems. Rev. Mat. Iberoam. 34 (2018), 195-220. doi: 10.4171/RMI/983