ABSTRACT
Discontinuous implicit elliptic
and parabolic problems
In this chapter we provide existence results for implicitly given parabolic dif-
ferential equations of the form H(x; t; u;u) = 0 subject to initial-Dirichlet
boundary conditions, where stands for some semilinear parabolic dier-
ential operator. The peculiarity of these implicit equations is that their
governing outer function H may be discontinuous in all its arguments and
that the parabolic operator is not necessarily inverse monotone. The
corresponding implicit elliptic problems are also discussed brie y.
