Global Hölder regularity for the fractional -Laplacian
Antonio Iannizzotto
Università degli Studi di Cagliari, ItalySunra J.N. Mosconi
Università degli Studi di Catania, ItalyMarco Squassina
Università Cattolica del Sacro Cuore, Brescia, Italy
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Abstract
By virtue of barrier arguments we prove -regularity up to the boundary for the weak solutions of a non-local, non-linear problem driven by the fractional -Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular () of degenerate () case.
Cite this article
Antonio Iannizzotto, Sunra J.N. Mosconi, Marco Squassina, Global Hölder regularity for the fractional -Laplacian. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1353–1392
DOI 10.4171/RMI/921