A One Dimensional Proof of the Hölder Inequality using the Heat Equation

2022/11/03 by Venkat Sripad Ganti, Ganti, Venkat Sripad
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2211.02123

openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a proof of the Hölder Inequality by using supersolutions of the Heat Equation. The proof is based on a monotonicity formula for the heat equation presented in Tobias Colding's lectures at MIT.

Related

• Generating monotone quantities for the heat equation
• Hölder's inequality: some recent and unexpected applications
• New Refinements for integral and sum forms of Hölder inequality
• A New Improvement of Hölder inequality via Isotonic Linear Functionals
• Hölder continuity for the p-Laplace equation using a differential inequality