On Fundamental Solutions and Gaussian Bounds for Degenerate Parabolic Equations with Time-dependent Coefficients

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-05-06 DOI:10.1007/s11118-024-10143-7

Alireza Ataei, Kaj Nyström

引用次数: 0

Abstract

We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial \(A_2\)-weight. We prove the existence of a fundamental solution and derive Gaussian bounds. Our construction is based on the original work of Kato (Nagoya Math. J. 19, 93–125 1961).

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论具有时变系数的畸变抛物方程的基本解和高斯边界

我们考虑的是二阶退化抛物方程，其系数为实数、可测量且随时间变化。我们允许由空间 \(A_2\)-weight 决定的退化椭圆性。我们证明了基本解的存在，并推导出高斯边界。我们的构造基于加藤（Kato）的原作（名古屋数学杂志 19, 93-125 1961）。

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.