ON THE DE RHAM COMPLEX ON A SCALE OF ANISOTROPIC WEIGHTED HOLDER SPACES

Abstract

We obtain a solvabilty criterion for the operator equations induced by de Rham differentials on a scale of anisotropic weighted Holder spaces on the strip Rⁿ × [0; T], n ≥ 1, where the weight controls the behavior of elements at the infinity point with respect to the space variables. Besides, we give a description of the closures in these space of the set of infinitely differentiable functions on the strip Rⁿ × [0; T] that are compactly supported with respect to the space variables. The results are applied to study the properties of the famous Leray-Helmholtz projection from the theory of the Navier-Stokes equations on the scale of these weighted spaces for n ≥ 2.