Regularity for solutions of non local, non symmetric equations

Details Regularity for solutions of non local, non symmetric equations Regularity for solutions of non local, non symmetric equations

2011-06-29

arxiv.org/abs/1106.6070v2

Mathematics

Analysis of PDEs

Scientific paper

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 part of the kernels have a fixed homogeneity $\sigma$ and the skew symmetric part have strictly smaller homogeneity $\tau$. 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.

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