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arXiv · 2602.07450

Traces of Sobolev functions and higher integrability

Robert Denk·Franz Gmeineder·Paul Stephan
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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.

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Robert Denk, Franz Gmeineder, Paul Stephan. 2026-02-07. Traces of Sobolev functions and higher integrability. https://arxiv.org/abs/2602.07450

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