论文标题
具有混合数据的非常奇异的准椭圆方程的加入梯度估计值
Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data
论文作者
论文摘要
本文将弱解决方案梯度梯度的边界建立到边界，并带有混合数据的一类非常单一的准椭圆方程：\ begin {case} - \ operatorname {div}（a（x，x，x，d u）= g- \ g- \ operatateName {div} f \ quad＆quad＆quad＆ud} \ text {on} \ \ partialω，\ end {case}其中$ω\ subset \ mathbb {r}^n $在Reifenberg的意义上就足够平坦。
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed data: \begin{cases} -\operatorname{div}(A(x,D u))=g-\operatorname{div} f \quad & \mathrm{in} \quad Ω\\ u= 0 \quad & \text{on} \ \partial Ω, \end{cases} where $Ω\subset \mathbb{R}^n$ is sufficiently flat in the sense of Reifenberg.
