no. 12
Partial Differential Equations
Convexity of solutions of parabolic equations
[Convexité des solutions d'équations paraboliques]

Présenté par : Pierre-Louis Lions

Lions, Pierre-Louis1, 2 ; Musiela, Marek3
1 Collège de France, 3, rue d'Ulm, 75005 Paris, France
2 Ceremade, UMR CNRS 7534, université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
3 FIRST, BNP PARIBAS, 10, Harewood Avenue, London NW1 6AA, UK
Comptes Rendus. Mathématique, Tome 342 (2006) no. 12, pp. 915-921.

Nous établissons dans cette note des conditions nécessaires et suffisantes pour la propagation de la convexité des solutions d'équations paraboliques. Nous considérons aussi bien des équations linéaires que complètement non linéaires. Et nous mentionnons diverses variantes et extensions de ces résultats.

We establish here necessary and sufficient conditions for the propagation of convexity in parabolic equations. We consider as well linear equations and fully nonlinear ones. And we discuss several variants and extensions of these results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.02.014
Lions, Pierre-Louis 1, 2 ; Musiela, Marek 3

1 Collège de France, 3, rue d'Ulm, 75005 Paris, France
2 Ceremade, UMR CNRS 7534, université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
3 FIRST, BNP PARIBAS, 10, Harewood Avenue, London NW1 6AA, UK 
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Lions, Pierre-Louis; Musiela, Marek. Convexity of solutions of parabolic equations. Comptes Rendus. Mathématique, Tome 342 (2006) no. 12, pp. 915-921. doi : 10.1016/j.crma.2006.02.014. http://archive.numdam.org/articles/10.1016/j.crma.2006.02.014/

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