C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
We establish Cs+a interior estimates for concave nonlocal fully nonlinear equations of order s¿(0,2) with rough kernels. Namely, we prove that if u¿Ca(Rn) solves in B1 a concave translation invariant equation with kernels in L0(s), then u belongs to (Formula Presented), with an estimate. More generally, our results allow the equation to depend on x in a Ca fashion. Our method of proof combines a Liouville theorem and a blow-up (compactness) procedure. Due to its flexibility, the same method can be useful in different regularity proofs for nonlocal equations.
CitationSerra, J. C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels. "Calculus of variations and partial differential equations", 01 Desembre 2015, vol. 54, p. 3571.