$C^{1,α}$ regularity for fully nonlinear elliptic equations with superlinear growth in the gradient

Gabrielle Nornberg

paper

$C^{1, α}$ regularity for fully nonlinear elliptic equations with superlinear growth in the gradient

arXiv:1802.01643

Abstract

We extend the Caffarelli-Świech-Winter $C^{1, α}$ 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 $W^{2, p}$ results, we prove the existence of positive eigenvalues for proper operators with nonnegative unbounded weight, in particular for Pucci's operators with unbounded coefficients.

arXiv comment32 pages, to appear in Journal de Mathématiques Pures et Appliquées

C1,α regularity for fully nonlinear elliptic equations with superlinear growth in the gradient

Abstract

$C^{1, α}$ regularity for fully nonlinear elliptic equations with superlinear growth in the gradient