High order symmetries of variations and nonlinear quasi-contractive estimates approach to the parabolic regularity problems

Abstract

The correct definition of differential operators and different mathematical objects naturally requires the construction of functional spaces of their action and the study of associated regularity problems. There is Cauchy-Liouville-Picard regularity scheme, created initially for the study of regular dependence of solutions to differential equations with respect to the initial data and different kind parameters.