An extensive study of the regularity properties of solutions to doubly singular equations

TL;DR

This paper provides a clear, concise, and comprehensive overview of the regularity properties of solutions to doubly singular equations, correcting previous inaccuracies and streamlining proofs for better understanding.

Contribution

It offers the first complete, self-contained, and simplified exposition of the regularity theory for doubly nonlinear singular evolution equations.

Findings

Corrected previous misprints and inaccuracies

Streamlined and simplified proofs of regularity results

Provided a comprehensive overview of the theory

Abstract

In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfluous assumptions or follow an inappropriate approximation procedure. This makes the theory unclear and quite chaotic to a nonspecialist. The aim of this paper is to fix all the misprints, to follow correct procedures, to exhibit, possibly, the shortest and most elegant proofs and to give a complete and self-contained overview of the theory.