The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption
G. C. Dong, B. J. Bian, Z. C. Guan
Abstract
Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation F(x,u, u, 2 u)=0, we establish the interior C1+1 continuity under the assumptions that F is uniformly elliptic, H older 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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