S\{o}ren Fournais, Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Thomas \{O}stergaard S\{o}rensen 
Sharp regularity 
 results for many-electron wave functions
(144K, LaTex2e)

ABSTRACT.  We show that electronic wave functions $\psi$ of atoms and molecules 
have a representation $\psi=\mathcal F \phi$, where $\mathcal F$ is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution $\psi$ itself, and $\phi$ has locally bounded second derivatives. This representation turns 
out to be optimal as can already be demonstrated with the help of hydrogenic wave functions. 
The proofs of these results are, in an essential way, based on a new 
elliptic regularity result which is of independent interest. Some identities that can be interpreted as cusp conditions for second order derivatives of $\psi$ are derived.