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We develop interior and regularity theories for -viscosity solutions to fully nonlinear elliptic equations , where T is approximately convex at infinity. Particularly, regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of are at least as . regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of regularity theory is dense in the space of fully nonlinear uniformly elliptic operators.
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Qingbo Huang, Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, pp. 1869–1902DOI 10.1016/J.ANIHPC.2019.06.001