Seminar

# Real analyticity of solutions to some nonlocal equations

#### Thomas Østergaard Sørensen - LMU Ludwig-Maximilians-Universität München

We prove (real) analyticity of solutions to certain nonlocal linear Schrödinger equations with analytic potentials, namely, $(-\Delta+m^2)^{s} \psi = V \psi$ for $$$s\in[1/2,1], m>0$$$ 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 $$$\sqrt{-\Delta+m^2}-m$$$. 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).
Organizers
Rafael D. Benguria