Geodesic
Mean curvature flow with obstacles: Existence, uniqueness and regularity of solutions
Gwenaël Mercier1 ; Matteo Novaga2 orcid
1Ecole Polytechnique, Palaiseau, France
2Università di Pisa, Italy
Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 399-426

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DOI

We show short time existence and uniqueness of C1,1 solutions to the mean curvature flow with obstacles, when the obstacles are of class C1,1. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.
DOI : 10.4171/ifb/348
Classification : 53-XX, 35-XX, 49-XX
Mots-clés : Mean curvature flow, obstacle problem, short time existence

Gwenaël Mercier  1   ; Matteo Novaga  2

1 Ecole Polytechnique, Palaiseau, France
2 Università di Pisa, Italy 
Gwenaël Mercier; Matteo Novaga. Mean curvature flow with obstacles: Existence, uniqueness and regularity of solutions. Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 399-426. doi: 10.4171/ifb/348
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     author = {Gwena\"el Mercier and Matteo Novaga},
     title = {Mean curvature flow with obstacles: {Existence,} uniqueness and regularity of solutions},
     journal = {Interfaces and free boundaries},
     pages = {399--426},
     year = {2015},
     volume = {17},
     number = {3},
     doi = {10.4171/ifb/348},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/348/}
}
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