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

TL;DR

This paper explores weighted H"older spaces tailored as a functional framework for analyzing the thin film equation and similar parabolic equations with boundary degeneracy, aiming to improve understanding of boundary behavior.

Contribution

It introduces specific weighted H"older spaces suitable for studying degenerate parabolic equations in multiple dimensions, expanding the analytical toolkit for such problems.

Findings

Weighted H"older spaces effectively model boundary degeneracy.

Framework applicable to various degenerate parabolic equations.

Potential for improved regularity results in boundary-degenerate problems.

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.