Continuity of a surface in Fréchet spaces

Ciarlet, Philippe G.; Malin, Maria; Mardare, Cristinel

doi:10.1016/j.crma.2019.10.010

Mathematical problems in mechanics/Differential geometry

Continuity of a surface in Fréchet spaces
[Continuité d'une surface dans des espaces de Fréchet]

Présenté par : Philippe G. Ciarlet

Ciarlet, Philippe G.¹ ; Malin, Maria ² ; Mardare, Cristinel ¹

¹ Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
² Department of Mathematics, University of Craiova, Craiova, 200585, Romania

Comptes Rendus. Mathématique, Tome 357 (2019) no. 11-12, pp. 917-921.

Résumé
Abstract

On établit la continuité d'une surface en fonction de ses deux premières formes fondamentales pour plusieurs topologies de Fréchet, qui incluent en particulier celles de l'espace $W_{loc}^{1, p}$ pour la première forme et de l'espace $L_{loc}^{p}$ pour la deuxième forme, où $p > 2$ .

We establish the continuity of a surface as a function of its first two fundamental forms for several Fréchet topologies, which include in particular those of the space $W_{loc}^{1, p}$ for the first fundamental form and of the space $L_{loc}^{p}$ for the second fundamental form, for any $p > 2$ .

Reçu le : 2019-10-18
Accepté le : 2019-10-18
Publié le : 2019-11-01

DOI : 10.1016/j.crma.2019.10.010

Affiliations des auteurs :

Ciarlet, Philippe G. ¹ ; Malin, Maria ² ; Mardare, Cristinel ¹

¹ Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
² Department of Mathematics, University of Craiova, Craiova, 200585, Romania

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     title = {Continuity of a surface in {Fr\'echet} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {917--921},
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Ciarlet, Philippe G.; Malin, Maria; Mardare, Cristinel. Continuity of a surface in Fréchet spaces. Comptes Rendus. Mathématique, Tome 357 (2019) no. 11-12, pp. 917-921. doi : 10.1016/j.crma.2019.10.010. http://www.numdam.org/articles/10.1016/j.crma.2019.10.010/

Bibliographie
Cité par

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[6] Ciarlet, P.G.; Mardare, C. A surface in $W^{2, p}$ is a locally Lipschitz-continuous function of its fundamental forms in $W^{1, p}$ and $L^{p}$ , $p > 2$ , J. Math. Pures Appl., Volume 124 (2019), pp. 300-318

[7] P.G. Ciarlet, M. Malin, C. Mardare, Continuity in Fréchet topologies of a surface as a function of its fundamental forms, in preparation.

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