Traces of Sobolev functions and higher integrability

Abstract

We give a sharp characterization of how additional integrability in the interior improves the integrability of boundary traces of ${\mathrm{W}}^{1,p}$-Sobolev functions. The optimality of our results relies on a novel nonlinear extension or lifting operator.

20 pages, 2 figures. Dedicated to Hans Triebel on the occasion of his 90th birthday