On a new transformation for generalised porous medium equations: from weak solutions to classical

TL;DR

This paper introduces a novel variable substitution for generalized porous medium equations that converts weak solutions, which are typically only Hölder continuous, into classical solutions, enhancing their regularity.

Contribution

The paper presents a new transformation method that improves the regularity of solutions to generalized porous medium equations from weak to classical.

Findings

Weak solutions are generally Hölder continuous.

The new substitution transforms weak solutions into classical solutions.

This approach potentially broadens the applicability of classical analysis techniques.

Abstract

It is well-known that solutions for generalised porous medium equations are, in general, only H\"older continuous. In this note, we propose a new variable substitution for such equations which transforms weak solutions into classical.