Continuity in H1-norms of surfaces in terms of the L1-norms of their fundamental forms |
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Authors: | Philippe G Ciarlet Liliana Gratie Cristinel Mardare |
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Institution: | 1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;3. Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France |
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Abstract: | The main purpose of this Note is to show how a ‘nonlinear Korn's inequality on a surface’ can be established. This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let ω be a domain in , let be a smooth immersion, and let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces stay uniformly away from zero; and finally, the three fundamental forms of the surfaces converge in toward the three fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as . To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). |
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