Uniformly elliptic boundary value problems

• Applicant: Professor Dr. Alexander Engel
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 510244757

Boundary value problems are an essential part of differential equations, and their study plays a considerable role in the field and has numerous applications to physics. Generalizing from domains in Euclidean space to manifolds with boundary (for example, if one is working in general relativity, then boundaries correspond to event horizons of black holes) the Atiyah-Patodi-Singer index theorem naturally comes into the game since it computes the Fredholm index of an elliptic operator via topological data together with the eta- invariant of the operator. The goal of this project is to bring the theory of elliptic boundary value problems to non-compact manifolds with possibly non-compact boundaries. This does not only allow us to study elliptic boundary value problems on non-compact domains in Euclidean space but also on, say, non-compact models for the universe like asymptotically Euclidean manifolds.

• DFG Programme: Research Grants