Sumati Surya (Raman Research Institute, Bangalore, India)
Ihsane Malass (Uni Potsdam)
We start by discussing Hodge theory on closed manifolds and the solvability of the differential equation du=f for f a given differential form. We then discuss the solvability of such problems on manifolds with boundary introducing an equivalent elliptical value problem, namely the Neumann problem after Spencer. For this purpose we use what can be understood as a generalisation of the Hodge theory to the case of manifolds with boundary.