论文标题
抛物线p-laplacian具有分数可不同的性能
The parabolic p-Laplacian with fractional differentiability
论文作者
论文摘要
我们研究了一个有限域中的抛物线$ p $ -laplacian系统。我们根据时空离散化推断了最佳的收敛速率，该速率基于时间的含义欧拉方案。我们的估计值是根据尼古斯基空间表示的，因此涵盖了解决方案（梯度）仅在时空中具有分数衍生物时的情况。主要新颖性是，与所有以前的结果不同，我们不假设空间和时间分辨率$ h $和$τ$之间的任何耦合条件。理论误差分析与数值实验相辅相成。
We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and therefore cover situations when the (gradient of) the solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolution $h$ and $τ$. The theoretical error analysis is complemented by numerical experiments.
