Abstract

We extend the Caffarelli-Swiech-Winter C-1,C-alpha regularity estimates to L-p-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form with superlinear growth in the gradient and unbounded coefficients. As an application, in addition to the usual W-2,W-P results, we prove the existence of positive eigenvalues for proper operators with nonnegative unbounded weight, in particular for Proper operators with unbounded coefficients. (C) 2019 Elsevier Masson SAS. All rights reserved.