论文标题
具有有界成分的完全非线性椭圆方程的潜在估计值
Potential estimates for fully nonlinear elliptic equations with bounded ingredients
论文作者
论文摘要
我们检查了具有有限测量成分的完全非线性椭圆方程的$ l^p $ - 粘度解决方案。通过考虑$ p_0 <p <d $，我们专注于非线性电位的梯度验证估计值。我们发现梯度解决方案和连续性的局部Lipschitz-continition条件。我们简要调查了（非线性）潜在估计引起的规律性理论的最新突破。我们的发现源于$ l^p $ viscosity解决方案理论的基本事实，并受到启发，并导致了Panagiota daskalopoulos，Tuomo Kuusi和Giuseppe Mingione的工作[10]。
We examine $L^p$-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $p_0<p<d$, we focus on gradient-regularity estimates stemming from nonlinear potentials. We find conditions for local Lipschitz-continuity of the solutions and continuity of the gradient. We briefly survey recent breakthroughs in regularity theory arising from (nonlinear) potential estimates. Our findings follow from -- and are inspired by -- fundamental facts in the theory of $L^p$-viscosity solutions, and results in the work of Panagiota Daskalopoulos, Tuomo Kuusi and Giuseppe Mingione [10].
