Approximation in Sobolev spaces of nonlinear expressions involving the gradient

Piotr Hajłasz Institute of Mathematics, Warsaw University Jan Malý Department of Mathematical Analysis, Charles University

TBD mathscidoc:1701.332984

Arkiv for Matematik, 40, (2), 245-274, 2001.2
We investigate a problem of approximation of a large class of nonlinear expressions$f$($x, u$, ∇$u$), including polyconvex functions. Here$u$: Ω→$R$^{$m$}, Ω⊂$R$^{$n$}, is a mapping from the Sobolev space$W$^{$1,p$}. In particular, when$p=n$, we obtain the approximation by mappings which are continuous, differentiable a.e. and, if in addition$n=m$, satisfy the Luzin condition. From the point of view of applications such mappings are almost as good as Lipschitz mappings. As far as we know, for the nonlinear problems that we consider, no natural approximation results were known so far. The results about the approximation of$f$($x, u$, ∇$u$) are consequences of the main result of the paper, Theorem 1.3, on a very strong approximation of Sobolev functions by locally weakly monotone functions.
No keywords uploaded!
[ Download ] [ 2017-01-08 20:36:04 uploaded by arkivadmin ] [ 147 downloads ] [ 0 comments ] [ Cited by 3 ]
@inproceedings{piotr2001approximation,
  title={Approximation in Sobolev spaces of nonlinear expressions involving the gradient},
  author={Piotr Hajłasz, and Jan Malý},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203604758338793},
  booktitle={Arkiv for Matematik},
  volume={40},
  number={2},
  pages={245-274},
  year={2001},
}
Piotr Hajłasz, and Jan Malý. Approximation in Sobolev spaces of nonlinear expressions involving the gradient. 2001. Vol. 40. In Arkiv for Matematik. pp.245-274. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203604758338793.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved