C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels

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Title:	C sigma+alfa regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels
Author:	Serra Montolí, Joaquim
Other authors:	Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Differential equations, Partial -35J60 -45K05 -Equacions diferencials parcials
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Document type:	Article - Submitted version Article
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