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arXiv · 1604.04442

Interior regularity for fractional systems

Luis Caffarelli·Gonzalo Davila
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Abstract

We study the regularity of solutions of elliptic fractional systems of order 2s, $s \in (0, 1)$, where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior Hölder estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [6] and M. Wiegner [9].

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Luis Caffarelli, Gonzalo Davila. 2016-04-15. Interior regularity for fractional systems. https://arxiv.org/abs/1604.04442

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