A reverse H\"older inequality for the gradient of solutions to Trudinger's equation

TL;DR

This paper establishes a higher integrability result for the gradient of positive solutions to Trudinger's equation, extending understanding of the equation's regularity properties for a broad range of p values.

Contribution

It introduces a refined method for constructing intrinsic cylinders, adapting scalar estimates to the vectorial setting to improve regularity results.

Findings

Higher integrability of the gradient for solutions to Trudinger's equation

Extension of regularity results to the range p ≥ 2

Refined construction of intrinsic cylinders for better estimates

Abstract

We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty)$. The estimate is achieved by refining a construction of intrinsic cylinders from the vectorial setting by incorporating estimates only available in the scalar case.