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- W2950243485 abstract "We prove the $C^{1}$ regularity and developability of $W^{2,p}$ isometric immersions of $n$-dimensional flat domains into ${mathbb R}^{n+k}$ where $pge min{2k, n}$. Another parallel consequence of our methods is a similar regularity and rigidity result for the $W^{2,n}$ solutions of the degenerate Monge-Amp`ere equations in $n$ dimensions. The analysis also applies to the situations when the degeneracy is extended to $(k+1)times (k+1)$ minors of the Hessian matrix and the solution is $W^{2,p}$, with $pge min{2k, n}$." @default.
- W2950243485 created "2019-06-27" @default.
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- W2950243485 date "2014-05-19" @default.
- W2950243485 modified "2023-09-27" @default.
- W2950243485 title "Sobolev spaces of isometric immersions of arbitrary dimension and codimension" @default.
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