@article{Hintermüller2015585,
title = "On the density of classes of closed convex sets with pointwise constraints in Sobolev spaces ",
journal = "Journal of Mathematical Analysis and Applications ",
volume = "426",
number = "1",
pages = "585 - 593",
year = "2015",
note = "",
issn = "0022-247X",
doi = "http://dx.doi.org/10.1016/j.jmaa.2015.01.060",
url = "http://www.sciencedirect.com/science/article/pii/S0022247X1500089X",
author = "M. Hintermüller and C.N. Rautenberg",
keywords = "Closed convex sets",
keywords = "Dense embedding",
keywords = "Gradients",
keywords = "Pointwise constraints",
keywords = "Sobolev spaces ",
abstract = "Abstract For a Banach space X of R M -valued functions on a Lipschitz domain, let K ( X ) ⊂ X be a closed convex set arising from pointwise constraints on the value of the function, its gradient or its divergence, respectively. The main result of the paper establishes, under certain conditions, the density of K ( X 0 ) in K ( X 1 ) where X 0 is densely and continuously embedded in X 1 . The proof is constructive, utilizes the theory of mollifiers and can be applied to Sobolev spaces such as H 0 ( div , Ω ) and W 0 1 , p ( Ω ) , in particular. It is also shown that such a density result cannot be expected in general. "
}