Thomas Østergaard Sørensen: Real analyticity of solutions to some nonlocal equations

We prove (real) analyticity of solutions to certain nonlocal linear Schrödinger equations with analytic potentials, namely,

(-Δ+m²)^s ψ = V ψ

for s ∈ [1/2,1], m > 0 and s=1/2, m=0. The method of the proof also allows to prove analyticity of solutions to the (nonlinear) Hartree-Fock equations for atoms and molecules with kinetic energy of the electrons equal to √(-Δ+m²) - m. We will also discuss the motivation for studying regularity in this case. This is joint work with A. Dall'Acqua (Magdeburg), S. Fournais (Aarhus), and E. Stockmeyer (Munich).