Regularity for solutions of nonlocal, nonsymmetric equations

Chang Lara, Héctor; Dávila, Gonzalo

Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012), p. 833-859 / Harvested from Numdam

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Résumé

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 $σ \to 2$ and $τ \to 1$ so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.

Publié le : 2012-01-01

MR 2995098 | Zbl 1317.35278

DOI : https://doi.org/10.1016/j.anihpc.2012.04.006

@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},
     volume = {29},
     year = {2012},
     pages = {833-859},
     doi = {10.1016/j.anihpc.2012.04.006},
     mrnumber = {2995098},
     zbl = {1317.35278},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 29 (2012) pp. 833-859. doi : 10.1016/j.anihpc.2012.04.006. http://gdmltest.u-ga.fr/item/AIHPC_2012__29_6_833_0/

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