  We study well-posedness for the relaxed linear elastic micromorphic continuum
model with symmetric Cauchy force-stresses and curvature contribution depending
only on the micro-dislocation tensor. In contrast to classical micromorphic
models our free energy is not uniformly pointwise positive definite in the
control of the independent constitutive variables. Another interesting feature
concerns the prescription of boundary values for the micro-distortion field:
only tangential traces may be determined which are weaker than the usual strong
anchoring boundary condition. There, decisive use is made of new coercive
inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff,
Pauly and Starke. The new relaxed micromorphic formulation can be related to
dislocation dynamics, gradient plasticity and seismic processes of earthquakes.
