Qualitative Theory of Equations and Inequalities with KPZ-nonlinearities

For quasilinear partial differential equations and inequalities containing nonlinearities of the Kardar-Parisi-Zhang type (i.e., the scalar square of the gradient andits generalizations), a summary of (old and recent) results regarding qualitative properties of solutions is presented. Descriptive examples demonstrating theBitsadze approach (the technique of monotone maps) applied in this researcharea are provided.