Questions about the trace map on Sobolev spaces, which maps a function on a domain to its boundary values, and generalizations or related concepts. Consider using [sobolev-spaces] as well. For questions about the trace of a matrix or other meanings of trace, please use [trace] instead.
This tag is for questions about or related to the trace map, $T$, which is a map that lets one talk about `boundary values' $Tu$ of a Sobolev function $u\in W^{1,p}(\Omega)$ where the boundary $\Omega\subset \mathbb R^n$ has some regularity. This makes sense despite the fact that $\partial\Omega$ is a null subset of $\mathbb R^n$; one cannot usually restrict a function defined almost everywhere to null sets.
A basic version of the Trace Theorem (proving the boundedness of $T:W^{1,p}(\Omega)\to L^p(\partial\Omega)$) for Lipschitz domains) can be found in Evans' "Partial Differential Equations". More general versions can be found in Adams and Fournier's "Sobolev Spaces".
Questions using this tag can be for example about a proof of the Trace Theorem, about the background needed to understand it, or applications to PDEs and other areas of mathematics. You should consider using the sobolev-spaces tag as well.
The word 'trace' has many other meanings in mathematics; for questions concerning the trace of elements in field extensions, use field-trace, and for others, use trace.
