论文标题
边界弱的harnack估计和椭圆形PDE的规律性发散形式
Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form
论文作者
论文摘要
我们获得了经典弱壁不平不平等的全局扩展，该扩展是扩展和量化Hopf-Oleinik边界点引理，以呈差异形式均匀地椭圆形方程。后果之一是一个边界梯度估计值，这是由于Krylov和对非发散形式方程式进行了充分研究，但在差异框架中是完全新颖的。另一个结果是Hopf-Oleinik引理的新型更通用版本。
We obtain a global extension of the classical weak Harnack inequality which extends and quantifies the Hopf-Oleinik boundary-point lemma, for uniformly elliptic equations in divergence form. Among the consequences is a boundary gradient estimate, due to Krylov and well-studied for non-divergence form equations, but completely novel in the divergence framework. Another consequence is a new more general version of the Hopf-Oleinik lemma.
