Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds

Fuente: arXiv
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Main Author: Sürig, Philipp
Format: Preprint
Published: 2023
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author Sürig, Philipp
author_facet Sürig, Philipp
contents We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial _{t}u=Δ_{p}(u^{1/(p-1)}), \end{equation*}% where $p>1$. This equation is also known as a doubly non-linear parabolic equation or Trudinger's equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including $\mathbb{R}^{n}$.
format Preprint
id arxiv_https___arxiv_org_abs_2309_01218
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds
Sürig, Philipp
Analysis of PDEs
Differential Geometry
We consider on Riemannian manifolds the nonlinear evolution equation \begin{equation*} \partial _{t}u=Δ_{p}(u^{1/(p-1)}), \end{equation*}% where $p>1$. This equation is also known as a doubly non-linear parabolic equation or Trudinger's equation. We prove that weak subsolutions of this equation have a sub-Gaussian upper bound and prove that this upper bound is sharp for a specific class of manifolds including $\mathbb{R}^{n}$.
title Sharp sub-Gaussian upper bounds for subsolutions of Trudinger's equation on Riemannian manifolds
topic Analysis of PDEs
Differential Geometry
url https://arxiv.org/abs/2309.01218