PreprintCC BY 4.0HAL
Upper and lower bounds for heat kernels with very strong degeneracy
Abstract
We consider the following degenerate parabolic equation on a bounded domain of ℝd containing $0$: $\partial_t u - \nabla\cdot(\varphi(t, x) \nabla u)= 0 $, where φ is a rough weight behaving like |x|θ near $0$ for some θ ≥ 2, and u satisfies Neumann boundary condition. We prove that this equation admits a heat kernel with upper and lower Gaussian-type bounds.
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BibTeX
@misc{bouton2026upper,
title = {{Upper and lower bounds for heat kernels with very strong degeneracy}},
author = {Hector Bouton},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29325},
eprint = {2610.29325},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05800356v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Upper and lower bounds for heat kernels with very strong degeneracy
AU - Hector Bouton
PY - 2026
DA - 2026/10/14
PB - HAL
DO - 10.48550/arxiv.2610.29325
UR - https://hal.science/hal-05800356v1
AB - We consider the following degenerate parabolic equation on a bounded domain of ℝ^d containing $0$: $\partial_t u - \nabla\cdot(\varphi(t, x) \nabla u)= 0 $, where φ is a rough weight behaving like |x|^θ near $0$ for some θ ≥ 2, and u satisfies Neumann boundary condition. We prove that this equation admits a heat kernel with upper and lower Gaussian-type bounds.
ER -