On Saint-Venant Compatibility and Stress Potentials in Manifolds with Boundary and Constant Sectional Curvature

We address three related problems in the theory of elasticity, formulated framework double forms: Saint-Venant compatibility condition, existence and uniqueness solutions for equations arising incompatible stress potentials. The scope this work is manifolds with boundary arbitrary dimension, having constant sectional curvature. central analytical machinery regular ellipticity a boundary-value problem bilaplacian operator, its consequences, which were developed [R. Kupferman R. Leder, arXiv:2103.16823, 2021]. One novelties that potentials can be used non-Euclidean geometries, gauge freedom exploited to obtain generalization biharmonic equation potential dimensions greater than two.