  We study many-body interaction effects in the spatially-resolved filling
factor ($\nu$) distribution for higher Landau levels (LLs) via self-consistent
Hartree-Fock simulations in the integer quantum Hall (IQH) regime. Our results
indicate a strong, interaction-induced tendency to avoid the simultaneous
existence of partially filled spin-up and spin-down LLs. Rather, we find that
such partially filled LLs consist of coexisting regions of full and empty LLs.
At the boundaries between the regions of full and empty LLs, we observe edge
stripes of nearly constant $\nu$ close to half-odd filling. This suggests that
the exchange interaction induces a behavior similar to a Hund's rule for the
occupation of the spin split LLs. The screening of the disorder and edge
potential appears significantly reduced as compared to static Thomas-Fermi
screening. Our results are consistent with a local, lateral $\nu$ dependence of
the exchange-enhanced spin splitting. Hence, on quantum-coherent length scales
as probed here, the electron system of the IQH effect behaves similar to a
non-interacting single particle system - not because of the absence, but rather
due to the dominance of many-body effects.
