In this article we give new conditions for the density of
continuous or smooth functions in variable exponent Sobolev
spaces. Our first result combines the previously known sufficient
conditions, a monotony condition by Edmunds and R#x00E1;kosn#x00ED;k and a
continuity condition independently due to Samko and Diening, into
a single weaker condition. The second main result gives a
sufficient condition in terms of the regularity of the level-sets
of the variable exponent.
Publié le : 2007-04-14
Classification:
variable exponent,
Sobolev spaces,
density of smooth functions,
density of continuous functions,
46E35,
26A15
@article{1180728891,
author = {H\"ast\"o, Peter A.},
title = {On the density of continuous functions in variable exponent Sobolev space},
journal = {Rev. Mat. Iberoamericana},
volume = {23},
number = {1},
year = {2007},
pages = { 213-234},
language = {en},
url = {http://dml.mathdoc.fr/item/1180728891}
}
Hästö, Peter A. On the density of continuous functions in variable exponent Sobolev space. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp. 213-234. http://gdmltest.u-ga.fr/item/1180728891/