Hölder continuity up to the boundary for a class of fractional obstacle problems

  • Tuomo Kuusi

    Aalto University, Finland
  • Janne Korvenpää

    Aalto University, Finland
  • Giampiero Palatucci

    Università degli Studi di Parma, Italy

Abstract

We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional -Laplacian with measurable coeffcients. In accordance with well-known results for the analog for the pure fractional Laplacian operator, the corresponding solutions inherit regularity properties from the obstacle, both in the case of boundedness, continuity, and Hölder continuity, up to the boundary.

Cite this article

Tuomo Kuusi, Janne Korvenpää, Giampiero Palatucci, Hölder continuity up to the boundary for a class of fractional obstacle problems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 3, pp. 355–367

DOI 10.4171/RLM/739