On some weighted H\"older spaces as a possible functional framework for the thin film equation and other parabolic equations with a degeneration at the boundary of a domain

Abstract

The present paper is devoted to studying of some weighted H\"older spaces. These spaces are designed in the way to serve as a framework for studying different statements for the thin film equations in weighted classes of smooth functions in the multidimensional setting. These spaces can serve also for considering of other equations with the degeneration on the boundary of the domain of definition.