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• W1744831645 abstract "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 $$pge min {2k, n}$$ . 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 $$k<n$$ , again assuming $$W^{2,p}_{mathrm{{loc}}}$$ regularity for $$pge min {2k,n}$$ . In particular, this includes results about the degenerate Monge–Ampère equation, $$mathrm{{det}} D^2 u = 0$$ , corresponding to the case $$k=n-1$$ ." @default.
• W1744831645 created "2016-06-24" @default.
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• W1744831645 date "2016-07-21" @default.
• W1744831645 modified "2023-10-03" @default.
• W1744831645 title "Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension" @default.
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• W1744831645 doi "https://doi.org/10.1007/s10231-016-0591-6" @default.
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