  A form of Sobolev inequalities for the symmetric gradient of vector-valued
functions is proposed, which allows for arbitrary ground domains in $\mathbb R
^n$. In the relevant inequalities, boundary regularity of domains is replaced
with information on boundary traces of trial functions. The inequalities so
obtained exhibit the same exponents as in classical inequalities for the full
gradient of Sobolev functions, in regular domains. Furthermore, they involve
constants independent of the geometry of the domain, and hence yield novel
results yet for smooth domains. Our approach relies upon a pointwise estimate
for the functions in question via a Riesz potential of their symmetric gradient
and an unconventional potential depending on their boundary trace.

Functional Analysis