Hölder continuity and Harnack estimate for non-homogeneous parabolic equations

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-08-30 DOI:10.1007/s00208-024-02979-6

Vedansh Arya, Vesa Julin

引用次数: 0

Abstract

In this paper we continue the study on intrinsic Harnack inequality for non-homogeneous parabolic equations in non-divergence form initiated by the first author in Arya (Calc Var Partial Differ Equ 61:30–31, 2022). We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the Hölder continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with Arya (2022) provides an alternative proof of the generalized Harnack inequality proven by the second author in Julin (Arch Ration Mech Anal 216:673–702, 2015).

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非均质抛物方程的荷尔德连续性和哈纳克估计

本文继续第一作者在 Arya (Calc Var Partial Differ Equ 61:30-31, 2022) 一文中发起的关于非发散形式非均质抛物方程的本征哈纳克不等式的研究。我们建立了一个前向时间内在哈纳克不等式，它尤其意味着解的赫尔德连续性。我们还提供了一个全局范围的哈纳克类型估计，它量化了强最小原则。在与时间无关的环境中，这与 Arya (2022) 一起为第二作者在 Julin（Arch Ration Mech Anal 216:673-702, 2015）中证明的广义哈纳克不等式提供了另一种证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.