Calculus of Variations and Geometric Measure Theory
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G. Mercier - M. Novaga

Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions

created by novaga on 24 Sep 2014
modified on 02 Jan 2018


Published Paper

Inserted: 24 sep 2014
Last Updated: 2 jan 2018

Journal: Interfaces and Free Boundaries
Volume: 17
Number: 3
Pages: 399-426
Year: 2015

ArXiv: 1409.7327 PDF


We show short time existence and uniqueness of $\C^{1,1}$ solutions to the mean curvature flow with obstacles, when the obstacles are of class $\C^{1,1}$. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.


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