Regularity of infinite dimensional heat dynamics of unbounded lattice spins with non-constant diffusion coefficients - Antoniouk, A.Val.; Antoniouk, A.Vict. (Інститут прикладної математики і механіки НАН України, 2007)
Below we demonstrate how the C^∞-regular properties of heat dynamics with non-unit nonlinear diffusion coefficient can be studied. We consider an infinite dimensional model, describing evolution of unbounded lattice spins R^Z^d. As a main step we provide a construction of corresponding variational processes in ℓp(c) spaces with growing weights ck ~ e^a|k|, k belongs Z^d. Developing the approach of nonlinear estimates on variations, we find sufficient conditions on the nonlinear coefficients of differential equation that lead to C^∞-regularity of solutions with respect to the initial data and C^∞-regularity of corresponding heat semigroup.