Approximation in Sobolev spaces of nonlinear expressions involving the gradient View Full Text


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Article Info

DATE

2002-10

AUTHORS

Piotr Hajłasz, Jan Malý

ABSTRACT

We investigate a problem of approximation of a large class of nonlinear expressionsf(x, u, ∇u), including polyconvex functions. Hereu: Ω→Rm, Ω⊂Rn, is a mapping from the Sobolev spaceW1,p. In particular, whenp=n, we obtain the approximation by mappings which are continuous, differentiable a.e. and, if in additionn=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 off(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. More... »

PAGES

245-274

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    http://scigraph.springernature.com/pub.10.1007/bf02384536

    DOI

    http://dx.doi.org/10.1007/bf02384536

    DIMENSIONS

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