论文标题
Edge凸平平滑插值曲线网络，最低$ l _ {\ infty} $ - 第二个衍生物的标准
Edge convex smooth interpolation curve networks with minimum $L_{\infty}$-norm of the second derivative
论文作者
论文摘要
我们考虑了$ \ Mathbb {r}^3 $在Smooth Edge Edge凸曲线网络中以最小$ l_p $ - 第二个导数的$ 1 <p \ p \ leq \ leq \ infty $的极端问题。 Andersson等人设定并解决了$ P = 2 $的问题。 （1995）。 Vlachkova（2019）在（Andersson等，1995）中扩展了结果，并以1美元的价格解决了该问题。从$ 1 <p <\ infty $的最小边缘凸出$ -L_P $ -NORM网络是从解决方案到具有数据系数的非线性方程系统的。对于严格凸数据，在情况下的解决方案$ 1 <p <\ infty $是唯一的。 $ p = \ infty $的相应极端问题保持开放。在这里，我们表明，$ p = \ infty $的极端插值问题总是有解决方案。我们给出了该解决方案的特征。我们表明，可以通过在其存在的情况下求解非线性方程系统来解决$ p = \ infty $的解决方案。
We consider the extremal problem of interpolation of convex scattered data in $\mathbb{R}^3$ by smooth edge convex curve networks with minimal $L_p$-norm of the second derivative for $1<p\leq\infty$. The problem for $p=2$ was set and solved by Andersson et al. (1995). Vlachkova (2019) extended the results in (Andersson et al., 1995) and solved the problem for $1<p<\infty$. The minimum edge convex $L_p$-norm network for $1<p<\infty$ is obtained from the solution to a system of nonlinear equations with coefficients determined by the data. The solution in the case $1<p<\infty$ is unique for strictly convex data. The corresponding extremal problem for $p=\infty$ remained open. Here we show that the extremal interpolation problem for $p=\infty$ always has a solution. We give a characterization of this solution. We show that a solution to the problem for $p=\infty$ can be found by solving a system of nonlinear equations in the case where it exists.
