Global Schauder Regularity and Convergence for Uniformly Degenerate Parabolic Equations

TL;DR

This paper investigates the regularity and long-term behavior of solutions to uniformly degenerate parabolic equations, establishing global Hölder regularity and convergence results under specific conditions.

Contribution

It provides new results on the global regularity and convergence of solutions to a class of degenerate parabolic equations, extending existing theory.

Findings

Established global Hölder regularity for solutions.

Proved convergence of solutions as time approaches infinity.

Identified conditions on characteristic exponents for convergence.

Abstract

In this paper, we study the global H\"older regularity of solutions to uniformly degenerate parabolic equations. We also study the convergence of solutions as time goes to infinity under extra assumptions on the characteristic exponents of the limit uniformly degenerate elliptic equations.