Potential estimates and improved Sobolev regularity for nonlocal fully nonlinear elliptic equations
Year: 2026
Type: preprint
Abstract: This paper investigates pointwise and oscillatory potential estimates for viscosity solutions and their gradients to a class of nonlocal fully nonlinear elliptic equations. The key ingredient of our argument is to establish precise pointwise bounds for a novel fractional sharp maximal function defined in terms of affine functions. As an immediate consequence, we prove higher order Sobolev regularity results of Calderón-Zygmund type for such equations without imposing any global boundedness assumptions on viscosity solutions. The potential theory developed herein extends the work of Daskalopoulos-Kuusi-Mingione (Commun. Partial Differ. Equ. 39: 574-590, 2014) for fully nonlinear second order elliptic equations to the fractional fully nonlinear setting.
Source: arXiv (Cornell University)
Authors: Zhang, Yao, Ma, Lingwei, Zhang, Zhenqiu
Institution: Nankai University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2483668369, G3520298065
OpenAlex ID: W7223322998