Geodesic
Regularity for solutions of nonlocal, nonsymmetric equations
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 6, pp. 833-859.

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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,α regularity. Our estimates remain uniform as we take σ→2 and τ→1 so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.

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     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},
     pages = {833--859},
     publisher = {Elsevier},
     volume = {29},
     number = {6},
     year = {2012},
     doi = {10.1016/j.anihpc.2012.04.006},
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     zbl = {1317.35278},
     language = {en},
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Chang Lara, Héctor; Dávila, Gonzalo. Regularity for solutions of nonlocal, nonsymmetric equations. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 6, pp. 833-859. doi : 10.1016/j.anihpc.2012.04.006. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.04.006/

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