论文标题
右侧的新边界竖琴不平等现象
New boundary Harnack inequalities with right hand side
论文作者
论文摘要
我们证明了Lipschitz域中的新边界不平等现象的右侧方程式。我们的主要结果适用于具有有限的可测量系数的非差异表单运算符，并且具有连续系数的Divergence表单运算符，而右侧的右侧为$ l^q $，带有$ q> n $。我们的方法基于\ cite {ds20}的缩放和比较论点，我们证明我们所有的假设都是敏锐的。 由于我们的结果，我们推断出$ \ MATHCAL {C}^{1，α} $在完全非线性障碍物问题和完全非线性的薄障碍物问题中的自由边界的规律性。
We prove new boundary Harnack inequalities in Lipschitz domains for equations with a right hand side. Our main result applies to non-divergence form operators with bounded measurable coefficients and to divergence form operators with continuous coefficients, whereas the right hand side is in $L^q$ with $q > n$. Our approach is based on the scaling and comparison arguments of \cite{DS20}, and we show that all our assumptions are sharp. As a consequence of our results, we deduce the $\mathcal{C}^{1,α}$ regularity of the free boundary in the fully nonlinear obstacle problem and the fully nonlinear thin obstacle problem.
