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On the moving plane method for nonlocal problems in bounded domains

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Abstract

We consider a nonlocal problem involving the fractional Laplacian and the Hardy potential in bounded smooth domains. Exploiting the moving plane method and some weak and strong comparison principles, we deduce symmetry and monotonicity properties of positive solutions under zero Dirichlet boundary conditions.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28009, Spain

    Begoña Barrios

  2. Dipartimento di Matematica e Informatica, Università della Calabria, Ponte Pietro Bucci 31B, I-87036, Arcavacata di Rende, Cosenza, Italy

    Luigi Montoro & Berardino Sciunzi

Authors
  1. Begoña Barrios
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  2. Luigi Montoro
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  3. Berardino Sciunzi
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Corresponding author

Correspondence to Berardino Sciunzi.

Additional information

Partially supported by project MTM2010-18128, MICI NN.

Partially supported by PRIN-2011: Variational and Topological Methods in the Study of Nonlinear Phenomena.

Partially supported by ERC-2011-grant: Elliptic PDE’ s and symmetry of interfaces and layers for odd nonlinearities.

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Barrios, B., Montoro, L. & Sciunzi, B. On the moving plane method for nonlocal problems in bounded domains. JAMA 135, 37–57 (2018). https://doi.org/10.1007/s11854-018-0031-1

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  • DOI: https://doi.org/10.1007/s11854-018-0031-1

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