Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 11 (2016), 2079-2154.
Boundary regularity for fully nonlinear integro-differential equations
We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order , with . We consider the class of nonlocal operators , which consists of infinitesimal generators of stable Lévy processes belonging to the class of Caffarelli–Silvestre. For fully nonlinear operators elliptic with respect to , we prove that solutions to in , in , satisfy , where is the distance to and . We expect the class to be the largest scale-invariant subclass of for which this result is true. In this direction, we show that the class is too large for all solutions to behave as . The constants in all the estimates in this article remain bounded as the order of the equation approaches . Thus, in the limit , we recover the celebrated boundary regularity result due to Krylov for fully nonlinear elliptic equations.
Duke Math. J., Volume 165, Number 11 (2016), 2079-2154.
Received: 2 April 2014
Revised: 23 August 2015
First available in Project Euclid: 16 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J60: Nonlinear elliptic equations
Secondary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Ros-Oton, Xavier; Serra, Joaquim. Boundary regularity for fully nonlinear integro-differential equations. Duke Math. J. 165 (2016), no. 11, 2079--2154. doi:10.1215/00127094-3476700. https://projecteuclid.org/euclid.dmj/1458133141