关于具有时间依赖系数的退化抛物方程的基本解与高斯估计
偏微分方程分析
2024-08-28 v3
摘要
我们考虑具有实的、可测的、时间依赖系数的二阶退化抛物方程。我们允许由空间 -权决定的退化椭圆性。我们证明了基本解的存在性并推导了高斯估计。我们的构造基于 Kato 的原创工作 \cite{Kato}。
引用
@article{arxiv.2303.02606,
title = {On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients},
author = {Alireza Ataei and Kaj Nyström},
journal= {arXiv preprint arXiv:2303.02606},
year = {2024}
}
备注
In this version, we have added more details in Section 3 of the paper. Section 3 contains the proof of the uniqueness part of our main result and as the argument uses Steklov averages and contains some subtleties, we now supply the full detail