Seminar

Real analyticity of solutions to some nonlocal equations

Hamiltonians in Magnetic Fields

01 November 14:00 - 15:00

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
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen