Variable exponent trace spaces

Lars Diening ¹   ; Peter Hästö ²

¹ Section of Applied Mathematics Freiburg University Eckerstrasse 1 79104 Freiburg/Breisgau, Germany
² Department of Mathematical Sciences P.O. Box 3000 FI-90014 University of Oulu, Finland

Studia Mathematica, Tome 183 (2007) no. 2, pp. 127-141

Résumé

The trace space of $W^{1,p(\cdot)}(\mathbb{R}^n\times [0,\infty))$ consists of those functions on $\mathbb{R}^n$ that can be extended to functions of $W^{1,p(\cdot)}(\mathbb{R}^n\times [0,\infty))$ (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.

Détail

DOI : 10.4064/sm183-2-3

Keywords: trace space cdot mathbb times infty consists those functions mathbb extended functions cdot mathbb times infty fixed exponent under assumption globally log h lder continuous trace space depends only values boundary main result define intrinsic norm trace space terms sharp type operator