Regularity for solutions of nonlocal, nonsymmetric equations
Héctor Chang Lara
University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX 78712, United StatesGonzalo Dávila
University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX 78712, United States
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Abstract
We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear operators where the symmetric parts of the kernels have a fixed homogeneity σ and the skew symmetric parts have strictly smaller homogeneity τ. We prove a weak ABP estimate and regularity. Our estimates remain uniform as we take and so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.
Cite this article
Héctor Chang Lara, Gonzalo Dávila, Regularity for solutions of nonlocal, nonsymmetric equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 6, pp. 833–859
DOI 10.1016/J.ANIHPC.2012.04.006