  We address three related problems in the theory of elasticity, formulated in
the framework of double forms: the Saint-Venant compatibility condition, the
existence and uniqueness of solutions for equations arising in incompatible
elasticity, and the existence of stress potentials. The scope of this work is
for manifolds with boundary of arbitrary dimension, having constant sectional
curvature. The central analytical machinery is the regular ellipticity of a
boundary-value problem for a bilaplacian operator, and its consequences, which
were developed in [KL21]. One of the novelties of this work is that stress
potentials can be used in non-Euclidean geometries, and that the gauge freedom
can be exploited to obtain a generalization for the biharmonic equation for the
stress potential in dimensions greater than two.
