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

Olli Saari; Sebastian Schwarzacher

doi:10.1007/s00030-022-00750-x

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

Analysis of PDEs 2022-03-22 v3

Authors: Olli Saari , Sebastian Schwarzacher

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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.

Keywords

reverse hölder inequality trudinger equation doubly nonlinear equation higher integrability intrinsic cylinders scalar case

Cite

@article{arxiv.1910.10498,
  title  = {A reverse H\"older inequality for the gradient of solutions to Trudinger's equation},
  author = {Olli Saari and Sebastian Schwarzacher},
  journal= {arXiv preprint arXiv:1910.10498},
  year   = {2022}
}

Comments

14 pages, referee comments incorporated, to appear in NoDEA

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