  We calculate the local density of states of a two-dimensional electron system
under strong crossed magnetic and electric fields. We assume a strong
perpendicular magnetic field which, in the absence of in-plane electric fields
and collision broadening effects, leads to Landau quantization and the
well-known singular Landau density of states. Unidirectional in-plane electric
fields lead to a broadening of the delta-function-singularities of the Landau
density of states. This results in position-dependent peaks of finite height
and width, which can be expressed in terms of the energy eigenfunctions. These
peaks become wider with increasing strength of the electric field and may
eventually overlap, which indicates the onset of inter-Landau-level scattering,
if electron-impurity scattering is considered. We present analytical results
for two simple models and discuss their possible relevance for the breakdown of
the integer quantized Hall effect. In addition, we consider a more realistic
model for an incompressible stripe separating two compressible regions, in
which nearly perfect screening pins adjacent Landau levels to the
electrochemical potential. We also discuss the effect of an imposed current on
the local density of states in the stripe region.
