chapter  7
24 Pages

Discontinuous implicit elliptic and parabolic problems

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.