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arXiv · 2207.06728

$ W^{\sigma,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations

Shuhei Kitano
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Abstract

$W^{\sigma,p}$ estimates are studied for a class of fully nonlinear integro-differential equations of order $\sigma$, which are analogues of $W^{2,p}$ estimates by Caffarelli. We also present Aleksandrov-Bakelman-Pucci maximum principles, which are improvements of estimates proved by Guillen-Schwab, depending only on $L^p$ norms of inhomogeneous terms.

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Shuhei Kitano. 2022-07-14. $ W^{\sigma,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations. https://doi.org/10.1007/s00526-022-02276-7

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