Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension

Autor:	Mohammad Reza Pakzad, Robert L. Jerrard
Rok vydání:	2016
Předmět:	Applied Mathematics 010102 general mathematics Degenerate energy levels Mathematical analysis Scalar (mathematics) Mathematics::Analysis of PDEs 01 natural sciences 010101 applied mathematics Sobolev space Combinatorics Geometric measure theory Bounded function 0101 mathematics Mathematics
Zdroj:	Annali di Matematica Pura ed Applicata (1923 -). 196:687-716
ISSN:	1618-1891 0373-3114
DOI:	10.1007/s10231-016-0591-6
Popis:	We prove the $$C^{1}_{\mathrm{{loc}}}$$ regularity and developability of $$W^{2,p}_{\mathrm{{loc}}}$$ isometric immersions of n-dimensional flat domains into $${\mathbb {R}}^{n+k}$$ where $$p\ge \min \{2k, n\}$$ . We also prove similar rigidity and regularity results for scalar functions of n variables for which the rank of the Hessian matrix is a.e. bounded by some $$k
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1ca64373bc8eff1f4b138c9fe3d4fe12 https://doi.org/10.1007/s10231-016-0591-6 Zobrazit plný text záznamu Full text from SpringerLink