We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional p-Laplacian with measurable coefficients. 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 Holder continuity, up to the boundary. Key words: Quasilinear nonlocal operators, fractional Sobolev spaces, nonlocal tail, Caccioppoli estimates, obstacle problem.
Holder continuity up to the boundary for a class of fractional obstacle problems / Korvenpää, Janne; Kuusi, Tuomo; Palatucci, Giampiero. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 27:3(2016), pp. 355-367. [10.4171/RLM/739]
Holder continuity up to the boundary for a class of fractional obstacle problems
PALATUCCI, Giampiero
2016-01-01
Abstract
We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional p-Laplacian with measurable coefficients. 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 Holder continuity, up to the boundary. Key words: Quasilinear nonlocal operators, fractional Sobolev spaces, nonlocal tail, Caccioppoli estimates, obstacle problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.