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 ${C}^{1,\alpha}$ regularity. Our estimates remain uniform as we take $\sigma \to 2$ and $\tau \to 1$ so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.

@article{AIHPC_2012__29_6_833_0, author = {Chang Lara, H\'ector and D\'avila, Gonzalo}, title = {Regularity for solutions of nonlocal, nonsymmetric equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {29}, number = {6}, year = {2012}, pages = {833-859}, doi = {10.1016/j.anihpc.2012.04.006}, zbl = {1317.35278}, mrnumber = {2995098}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2012__29_6_833_0} }

Chang Lara, Héctor; Dávila, Gonzalo. Regularity for solutions of nonlocal, nonsymmetric equations. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 6, pp. 833-859. doi : 10.1016/j.anihpc.2012.04.006. http://www.numdam.org/item/AIHPC_2012__29_6_833_0/

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