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The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption

G. C. Dong·B. J. Bian·Z. C. Guan
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Abstract

Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation $$F(x,u,\triangledown u,\triangledown ^2 u)=0,$$ we establish the interior $C^{1+1}$ continuity under the assumptions that $F$ is uniformly elliptic, H$\ddot o$lder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of $F$. These assumptions are weaker and the result is stronger than that of Caffarelli and Wang[1], Chen[2].

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G. C. Dong, B. J. Bian, Z. C. Guan. 2005-06-24. The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption. https://arxiv.org/abs/math/0506494

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