Year: 2026
Type: preprint
Abstract: We consider the following degenerate parabolic equation on a bounded domain of $\mathbb{R}^d$ containing $0$: $\partial_t u - \nabla\cdot(φ(t, x) \nabla u)= 0$, where $φ$ is a rough weight behaving like $|x|^θ$ near $0$ for some $θ\geq 2$, and $u$ satisfies Neumann boundary condition. We prove that this equation admits a heat kernel with upper and lower Gaussian-type bounds.
Source: arXiv (Cornell University)
Author: Bouton, Hector
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223190120