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

2018/02/05 by Gabrielle Nornberg, Nornberg, Gabrielle · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1802.01643

32 pages, to appear in Journal de Mathématiques Pures et Appliquées

arxiv created 2019/07/05 · arxiv updated 2019/07/08

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.

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• Estimates for viscosity solutions of fully nonlinear equations near smooth boundaries

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