W2,p -estimates for surfaces in terms of their two fundamental forms

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Original languageEnglish
Pages (from-to)85-91
Journal / PublicationComptes Rendus Mathematique
Issue number1
Online published19 Dec 2017
Publication statusPublished - Jan 2018



Let p>2. We show how the fundamental theorem of surface theory for surfaces of class W2,ploc(ω) over a simply-connected open subset of R2 established in 2005 by S. Mardare can be extended to surfaces of class W2,p(ω) when ω is in addition bounded and has a Lipschitz-continuous boundary. Then we establish a nonlinear Korn inequality for surfaces of class W2,p(ω). Finally, we show that the mapping that defines in this fashion a surface of class W2,p(ω), unique up to proper isometries of E3, in terms of its two fundamental forms is locally Lipschitz-continuous.

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