scholarly journals Convergence of space-time discrete threshold dynamics to anisotropic motion by mean curvature

2016 ◽  
Vol 36 (11) ◽  
pp. 6379-6411
Author(s):  
Nung Kwan Yip ◽  
Oleksandr Misiats
Keyword(s):  
Mean Curvature ◽  
Space Time ◽  
Threshold Dynamics ◽  
Anisotropic Motion ◽  
Motion By Mean Curvature

APPROXIMATION AND COMPARISON FOR NONSMOOTH ANISOTROPIC MOTION BY MEAN CURVATURE IN ℝN

2000 ◽  
Vol 10 (01) ◽  
pp. 1-10 ◽  
Author(s):  
G. BELLETTINI ◽  
M. NOVAGA
Keyword(s):  
Comparison Theorem ◽  
Mean Curvature ◽  
Driving Force ◽  
Space Dimension ◽  
Reaction Diffusion ◽  
Optimal Approximation ◽  
Time Dependent ◽  
Anisotropic Motion ◽  
Motion By Mean Curvature ◽  
Regular Flow

We prove that a reaction-diffusion inclusion provides a sub-optimal approximation for anisotropic motion by mean curvature in the nonsmooth case. This result is valid in any space dimension and with a time-dependent driving force, provided we assume the existence of a regular flow. The crystalline case is included. As a by-product of our analysis, a comparison theorem between regular flows is obtained. This result implies uniqueness of the original flow.

scholarly journals Second order threshold dynamics schemes for two phase motion by mean curvature

2020 ◽  
Vol 410 ◽  
pp. 109404
Author(s):  
Alexander Zaitzeff ◽  
Selim Esedoḡlu ◽  
Krishna Garikipati
Keyword(s):  
Mean Curvature ◽  
Second Order ◽  
Threshold Dynamics ◽  
Two Phase ◽  
Motion By Mean Curvature ◽  
Phase Motion
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