We consider a Klein-Gordon equation on asymptotically anti-de Sitter spacetimes subject to a very general class of boundary conditions implemented on the conformal boundary by pseudodifferential operators. Using microlocal estimates, we prove a propagation of singularities theorem along generalized broken bicharacteristics and we study the well-posedness of the problem, proving existence and uniqueness theorems for a subset of the boundary conditions considered that includes interesting cases: In particular among this class of boundary conditions, in addition to Neumann, Dirichlet and Robin, there are dynamical boundary conditions (e.g. of Wentzell kind).
This talk is part of series of talks affiliated with the virtual Mittag-Leffler workshop "Scattering, microlocal analysis and renormalization", organized by Claudio Dappiaggi, Jacob Schach Møller and Michal Wrochna. The full schedule can be found at: