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

2023/09/03 by Philipp Sürig, Sürig, Philipp · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.01218

openalex publication_date 2023/09/03 · openalex created_date 2023/09/08 · openalex updated_date 2026/08/01

Abstract

We consider on Riemannian manifolds the nonlinear evolution equation ∂ _tu=Δ_p(u^1/(p-1)),% 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 ℝⁿ.

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• The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation

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