Regularity properties of isometric immersions

Stefan Müller and Mohammed Reza Pakzad
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Submission date: 28. Jan. 2004
Pages: 24
published in: Mathematische Zeitschrift, 251 (2005) 2, p. 313-331 
DOI number (of the published article): 10.1007/s00209-005-0804-y
MSC-Numbers: 53C42, 35B65, 74K20, 53A05
Keywords and phrases: isometric immersion, regularity, rigidity, plates
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Abstract:
We show that an isometric immersion y from a two-dimensional domain S with boundary to which belongs to the critical Sobolev space is up to the boundary. More generally regularity up to the boundary holds for all scalar functions which satisfy . If S has only Lipschitz boundary we show such V can be approximated in by functions with .