no. 17-18
Partial Differential Equations
Uniqueness of unbounded solutions of the Lagrangian mean curvature flow equation for graphs
[Unicité des solutions non bornées du flot lagrangien à courbure moyenne pour les graphes]

Présenté par : Pierre-Louis Lions

Chen, Jingyi1 ; Pang, Chao1
1 Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada
Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1031-1034.

Nous remarquons que le résultat de comparaison de Barles–Biton–Ley sur les solutions de viscosité d'une classe d'équations non linéaires paraboliques peut être appliqué à une équation géométrique, complètement non linéaire parabolique qui apparaît dans les solutions graphiques pour les flots Lagrangiens à courbure moyenne.

We observe that the comparison result of Barles–Biton–Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.06.020
Chen, Jingyi 1 ; Pang, Chao 1

1 Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada 
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Chen, Jingyi; Pang, Chao. Uniqueness of unbounded solutions of the Lagrangian mean curvature flow equation for graphs. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1031-1034. doi : 10.1016/j.crma.2009.06.020. http://www.numdam.org/articles/10.1016/j.crma.2009.06.020/

[1] Barles, G.; Biton, S.; Ley, O. Uniqueness for parabolic equations without growth condition and applications to the mean curvature flow in R2, J. Differential Equations, Volume 187 (2003), pp. 456-472

[2] Chau, A.; Chen, J.; He, W. Lagrangian mean curvature flow for entire Lipschitz graphs | arXiv

[3] Crandall, M.G.; Ishii, H.; Lions, P.-L. User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., Volume 27 (1992), pp. 1-67

[4] Horn, R.A.; Johnson, C.R. Matrix Analysis, Cambridge University Press, 1985

[5] Smoczyk, K. Longtime existence of the Lagrangian mean curvature flow, Calc. Var., Volume 20 (2004), pp. 25-46

[6] Smoczyk, K.; Wang, M.T. Mean curvature flow of Lagrangian submanifolds with convex potentials, J. Differential Geom., Volume 62 (2002), pp. 243-257

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