  Most Mott systems display a low-temperature phase coexistence region around
the metal-insulator transition. The domain walls separating the respective
phases have very recently been observed both in simulations and in experiments,
displaying unusual properties. First, they often cover a significant volume
fraction, thus cannot be neglected. Second, they neither resemble a typical
metal nor a standard insulator, displaying unfamiliar temperature dependence of
(local) transport properties. Here we take a closer look at such domain wall
matter by examining an appropriate unstable solution of the Hubbard model. We
show that transport in this regime is dominated by the emergence of "resilient
quasiparticles" displaying strong non-Fermi liquid features, reflecting the
quantum-critical fluctuations in the vicinity of the Mott point.
