$W^{\sigma,\epsilon}$-estimates for nonlocal elliptic equations

Hui Yu

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arXiv · 1601.05882

$W^{\sigma,\epsilon}$-estimates for nonlocal elliptic equations

Hui Yu

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Abstract

We prove that the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order equations, by first proving a potential estimate, then combining this estimate with the ABP-type estimate by N. Guillen and R. Schwab to control the size of the superlevel sets of the fractional derivatives of solutions.

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Hui Yu. 2016-01-22. $W^{\sigma,\epsilon}$-estimates for nonlocal elliptic equations. https://arxiv.org/abs/1601.05882

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