Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms

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In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms.

• In particular, the equations with quadratic growth (called natural growth) in the gradient are covered.
• We obtain a series of interior and boundary pointwise $C^{k,\alpha}$ regularity ($k\geq 1$ and $0<\alpha<1$).
• In addition, we also derive the pointwise $C^k$ regularity ($k\geq 1$) and $C^{k,\mathrm{lnL}}$ regularity ($k\geq 0$), which correspond to the end points $\alpha=0$ and $\alpha=1$ respectively.