Nonlinear effects in the regularity problems for infinite dimensional evolutions of unbounded spin systems

Abstract

We study the regularity problems for unbounded spin systems of anharmonic oscillators, that approximate multi-dimensional Euclidean field theories. The main attention is paid to the effect of anharmonism on the C ∞ -regularity properties of evolutional semigroup. Our approach is based on a new class of nonlinear estimates on variations, that permit to obtain regular properties for essentially nonlinear equations.