JournalsrmiVol. 34, No. 1pp. 195–220

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

  • Begoña Barrios

    University of Texas at Austin, USA

  • Leandro M. Del Pezzo

    CONICET and Universidad de Buenos Aires, Argentina

  • Jorge García-Melián

    Universidad de La Laguna, Tenerife, Spain

  • Alexander Quaas

    Universidad Técnica Federico Santa María, Valparaíso, Chile
A priori bounds and existence of solutions for some nonlocal elliptic problems cover
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Abstract

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.

Cite this article

Begoña Barrios, Leandro M. Del Pezzo, Jorge García-Melián, Alexander Quaas, A priori bounds and existence of solutions for some nonlocal elliptic problems. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 195–220

DOI 10.4171/RMI/983