凸域上Neumann热核及其迹的均衡估计
偏微分方程分析
2026-01-13 v1 谱理论
摘要
我们证明了凸域上Neumann Laplacian热迹的下界，捕捉其小时间展开的前两项，但对所有时间都有效，且仅依赖于基本几何特征。通过对边界附近的脊缘热核的精确均衡展开来证明。我们的结果大多数情况下在无凸性假设下也成立，同时也考虑Lipschitz域的热迹两项渐近分析。
引用
@article{arxiv.2601.07341,
title = {Uniform bounds for Neumann heat kernels and their traces in convex sets},
author = {Rupert L. Frank and Simon Larson},
journal= {arXiv preprint arXiv:2601.07341},
year = {2026}
}
备注
The paper extends part of what was contained in an earlier version of arXiv:2407.11808