# Geometric tangential analysis and sharp regularity for degenerate pdes

## TL;DR

This paper reviews qualitative and quantitative regularity estimates for degenerate parabolic pdes, highlighting methods like intrinsic scaling and geometric tangential analysis, with sharp results for key equations.

## Contribution

It provides a comprehensive overview of regularity techniques, emphasizing the role of geometric tangential analysis in obtaining sharp estimates for degenerate pdes.

## Key findings

- Sharp regularity estimates for the parabolic p-Poisson equation
- Enhanced understanding of porous medium equation regularity
- Application of geometric tangential analysis to doubly nonlinear equations

## Abstract

We provide a broad overview on qualitative versus quantitative regularity estimates in the theory of degenerate parabolic pdes. The former relates to DiBenedetto's revolutionary method of intrinsic scaling, while the latter is achieved by means of what has been termed geometric tangential analysis. We discuss, in particular, sharp estimates for the parabolic p-Poisson equation, for the porous medium equation and for the doubly nonlinear equation.