Content:
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 (div,Ω) and W1,p(Ω), in particular. It is also shown that such a density result cannot be expected in general.
Content:
Peer Reviewed
Note:
This is the preprint version of the final publication with doi j.jmaa.2015.01.060, whichcan be found at Elsevier:https://doi.org/10.1016/j.jmaa.2015.01.060
In:
Journal of Mathematical Analysis and Applications, : Elsevier, 2015, 426,2015,1, Seiten 585-593
Language:
English
URN:
urn:nbn:de:kobv:11-100246628
URL:
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