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

G. C. Dong; B. J. Bian; Z. C. Guan

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

偏微分方程分析 2007-05-23 v1

作者: G. C. Dong , B. J. Bian , Z. C. Guan

摘要

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].

关键词

regularity for elliptic equations regularity of solutions parabolic equations

引用

@article{arxiv.math/0506494,
  title  = {The Second Order Estimate for Fully Nonlinear Uniformly Elliptic Equations without Concavity Assumption},
  author = {G. C. Dong and B. J. Bian and Z. C. Guan},
  journal= {arXiv preprint arXiv:math/0506494},
  year   = {2007}
}

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25pages

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

摘要

关键词

引用

备注

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