论文标题
Lipschitz的矢量线性传输问题的规律性
Lipschitz Regularity in Vectorial Linear Transmission Problems
论文作者
论文摘要
我们考虑到线性传输问题的矢量值解决方案，我们证明了一个阶段的Lipschitz-renformunity是传递到下一阶段的。更确切地说，给定的解决方案$ u：b_1 \ subset \ mathbb {r}^n \ to \ m athbb {r}^m $ to Elliptic System \ begin \ begin {equination*} \ mbox {div}（div}（（a +（a +（a +（a +））其中$ a $和$ b $是dini连续的，均匀的椭圆矩阵，我们证明，如果$ \ nabla u \ in l^{\ infty}（d）$ in $ u $是$ b_ {1/2} $的$ u $。对于此问题的抛物线对应物，也得出了类似的结果。
We consider vector-valued solutions to a linear transmission problem, and we prove that Lipschitz-regularity on one phase is transmitted to the next phase. More exactly, given a solution $u:B_1\subset \mathbb{R}^n \to \mathbb{R}^m$ to the elliptic system \begin{equation*} \mbox{div} ((A + (B-A)χ_D )\nabla u) = 0 \quad \text{in }B_1, \end{equation*} where $A$ and $B$ are Dini continuous, uniformly elliptic matrices, we prove that if $\nabla u \in L^{\infty} (D)$ then $u$ is Lipschitz in $B_{1/2}$. A similar result is also derived for the parabolic counterpart of this problem.
