The book Linear and Quasilinear equations of parabolic type gives the uniform parabolic pde theory in the literature. Ladyzhenskaya use Leray-Schauder rather than Schauder fixed point theorem. why? When would one use Leray-Schauder over Schauder fixed point? I don't understand why ladyzenskaya chosen to use Leray-Schauder over Schauder fixed-point theorem.
Appreciate any comments.