Geodesic
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.

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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.

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.

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://geodesic.mathdoc.fr/articles/10.1016/j.crma.2009.06.020/

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[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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