Title: Nonlinear effects in the regularity problems for infinite dimensional evolutions of unbounded spin systems
Author(s):

	Alexander Val. Antoniouk (Department of Nonlinear Analysis, Institute of Mathematics NAS Ukraine, Tereschenkivska 3, 01601 MSP, Kiev 4, Ukraine) ,
	Alexandra Vict. Antoniouk (Department of Nonlinear Analysis, Institute of Mathematics NAS Ukraine, Tereschenkivska 3, 01601 MSP, Kiev 4, Ukraine)

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.

Key words: anharmonic lattice spin systems, nonlinear regularity problems
PACS: 02.30.Jr, 02.30.Sa, 02.30.Xx, 02.50.Eu,03.654.Db, 05.50.+q, 75.10.Hk