Nonlinear-estimate approach to the regularity of infinite-dimensional parabolic problems

Abstract

We show how the use of nonlinear symmetries of higher-order derivatives allows one to study the regularity of solutions of nonlinear differential equations in the case where the classical Cauchy-Liouville-Picard scheme is not applicable. In particular, we obtain nonlinear estimates for the boundedness and continuity of variations with respect to initial data and discuss their applications to the dynamics of unbounded lattice Gibbs models.