论文标题
一般形式的完全非线性椭圆方程的定期
Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms
论文作者
论文摘要
在本文中，我们系统地开发了通用形式的完全非线性椭圆方程的粘度解的点上规律性。特别是，涵盖了梯度中具有二次增长（称为自然生长）的方程式。我们获得了一系列内部和边界，$ c^{k，α} $ juromity（$ k \ geq 1 $和$ 0 <α<1 $）。此外，我们还得出了$ c^k $ juromentity（$ k \ geq 1 $）和$ c^{k，\ m atrm {lnl}} $ juromistity（$ k \ geq 0 $），该终点分别对应于终点$α= 0 $和$α= 1 $。即使对于线性方程，一些规律性结果也是新的。此外，最低要求要获得以上规律性，我们的证明很简单。
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 $C^{k,α}$ regularity ($k\geq 1$ and $0<α<1$). 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 $α=0$ and $α=1$ respectively. Some regularity results are new even for the linear equations. Moreover, the minimum requirements are imposed to obtain above regularity and our proofs are simple.
