  In this work we study the $3+1$-dimensional Nambu-Jona-Lasinio (NJL) model in
the mean field-approximation. We carry out calculations using five different
regularization schemes (two continuum and three lattice regularization schemes)
with particular focus on inhomogeneous phases and condensates. The
regularization schemes lead to drastically different inhomogeneous regions. We
provide evidence that inhomogeneous condensates appear for all regularization
schemes almost exclusively at values of the chemical potential and with wave
numbers, which are of the order of or even larger than the corresponding
regulators. This can be interpreted as indication that inhomogeneous phases in
the $3+1$-dimensional NJL model are rather artifacts of the regularization and
not a consequence of the NJL Lagrangian and its symmetries.
