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Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions

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Abstract

We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting.

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Authors and Affiliations

  1. Dipartimento di Ecologia e Biologia (DEB), Università della Tuscia, Largo dell’Università, 01100, Viterbo, Italy

    Dimitri Mugnai

  2. Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38123, Povo, Trento, Italy

    Andrea Pinamonti

  3. Dipartimento di Matematica, Politecnico di Milano, Via Edoardo Bonardi 13, 20133, Milan, Italy

    Eugenio Vecchi

Authors
  1. Dimitri Mugnai
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  2. Andrea Pinamonti
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  3. Eugenio Vecchi
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Correspondence to Andrea Pinamonti.

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Communicated by P. Rabinowitz.

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Mugnai, D., Pinamonti, A. & Vecchi, E. Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions. Calc. Var. 59, 43 (2020). https://doi.org/10.1007/s00526-020-1708-8

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