Intrinsic Harnack’s Inequality for a General Nonlinear Parabolic Equation in Non-divergence Form

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-04-25 DOI:10.1007/s11118-024-10141-9

Tapio Kurkinen, Jarkko Siltakoski

引用次数: 0

Abstract

We prove the intrinsic Harnack’s inequality for a general form of a parabolic equation that generalizes both the standard parabolic p-Laplace equation and the normalized version arising from stochastic game theory. We prove each result for the optimal range of exponents and ensure that we get stable constants.

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非发散形式一般非线性抛物方程的本征哈纳克不等式

我们证明了抛物线方程一般形式的本征哈纳克不等式，该方程概括了标准抛物线 p-Laplace 方程和随机博弈论中出现的归一化版本。我们为指数的最佳范围证明了每个结果，并确保得到稳定的常数。

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

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.