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arXiv · 1006.0608

Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels : Subcritical Case

Yong-Cheol Kim·Ki-Ahm Lee
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Abstract

We introduce a new class of fully nonlinear integro-differential operators with possible nonsymmetric kernels, which includes the ones that arise from stochastic control problems with purely jump L\`evy processes. If the index of the operator $\sigma$ is in $ (1,2)$ (subcritical case), then we obtain a comparison principle, a nonlocal version of the Alexandroff-Backelman-Pucci estimate, a Harnack inequality, a H\"older regularity, and an interior $\rm C^{1,\alpha}$-regularity for fully nonlinear integro-differential equations associated with such a class. Moreover, our estimates remain uniform as the index $\sigma$ of the operator is getting close to two, so that they can be regarded as a natural extension of regularity results for elliptic partial differential equations.

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Yong-Cheol Kim, Ki-Ahm Lee. 2010-06-03. Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels : Subcritical Case. https://arxiv.org/abs/1006.0608

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