论文标题
Willmore功能和Willmore流的“无梯度”弥散近似
"Gradient-free" diffuse approximations of the Willmore functional and Willmore flow
论文作者
论文摘要
我们介绍了Willmore功能和Willmore流的新扩散近似值。它们基于由Amstutz-Van Goethem [{\ em Interfaces nood Bound Bond Bound Bond Bound Bond Bonder body body'所研究的周长的相应近似。 14（2012）}]。我们确定了$γ$的候选人 - 融合，证明$γ$ - limsup声明，并通过渐近扩张来证明融合到威尔莫尔流量的合理性。此外，我们提出基于新近似值的数值模拟。
We introduce new diffuse approximations of the Willmore functional and the Willmore flow. They are based on a corresponding approximation of the perimeter that has been studied by Amstutz-van Goethem [{\em Interfaces Free Bound. 14 (2012)}]. We identify the candidate for the $Γ$--convergence, prove the $Γ$--limsup statement and justify the convergence to the Willmore flow by an asymptotic expansion. Furthermore, we present numerical simulations that are based on the new approximation.
