Variable exponent trace spaces

Lars Diening; Peter Hästö

Studia Mathematica, Tome 178 (2007), p. 127-141 / Harvested from The Polish Digital Mathematics Library

Résumé

The trace space of $W^{1, p (\cdot)} (ℝ ⁿ \times [0, \infty))$ consists of those functions on ℝⁿ that can be extended to functions of $W^{1, p (\cdot)} (ℝ ⁿ \times [0, \infty))$ (as in the fixed-exponent case). Under the assumption that p is globally log-Hölder continuous, we show that the trace space depends only on the values of p on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.

Publié le : 2007-01-01

Zbl 1134.46016

EUDML-ID : urn:eudml:doc:285000

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-3,
     author = {Lars Diening and Peter H\"ast\"o},
     title = {Variable exponent trace spaces},
     journal = {Studia Mathematica},
     volume = {178},
     year = {2007},
     pages = {127-141},
     zbl = {1134.46016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-3}
}

Lars Diening; Peter Hästö. Variable exponent trace spaces. Studia Mathematica, Tome 178 (2007) pp. 127-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-2-3/