On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients
Analysis of PDEs
2024-08-28 v3
Abstract
We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial -weight. We prove the existence of a fundamental solution and derive Gaussian bounds. Our construction is based on the original work of Kato \cite{Kato}.
Keywords
Cite
@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}
}
Comments
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