A Regularity Result of Nikolskii Type for an Evolution Equation on Compact Homogeneous Spaces

In the previous paper [2], we proposed a definition of a class of function spaces of Nikolskii type on a special class of riemannian manifolds, namely the manifolds M admitting a transitive compact connected Lie group of isometries. In this paper we continue the subject and we complete the proof that the spaces we have introduced coincide with the classical ones, defined through (finitely many) local charts of M. Moreover, our equivalent definition of these spaces allows us to prove here a regularity result for the solution of a Stefan-like problem on M, in which the initial datum is assumed to be of Nikolskii type.