PreprintCC BY 4.0arXiv
Calculations for a general maximum principle: 1993 notes on the normalized parabolic p-Laplacian
Abstract
This note makes available, in facsimile form, a set of handwritten notes from September 1993 devoted to Bochner-type maximum principle computations for a general class of quasilinear parabolic equations which contains, as a special instance, the normalized parabolic p-Laplacian ut = Δu + (p−2) |∇ u|−2 ∇2u(∇ u,∇ u). The notes were acknowledged in the introduction of the paper of Jin and Silvestre \cite{JS}, and the scheme they propose has recently been implemented in \cite{BGM} to obtain the sharp Li-Yau inequality for this equation. They are reproduced here verbatim, with no alterations, preceded by a brief introduction explaining their content and the subsequent history of the equation.
Related
- Time derivative estimates for normalized parabolic p-Laplace equations
- Faber--Krahn inequality for homogeneous normalized p-Laplacian type operators
- Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
- Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations
- Hölder regularity of solutions to parabolic equations associated with fractional p-Laplacian type operators
BibTeX
@misc{garofalo2026calculations,
title = {{Calculations for a general maximum principle: 1993 notes on the normalized parabolic $p$-Laplacian}},
author = {Nicola Garofalo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13209},
eprint = {2609.13209},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13209},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calculations for a general maximum principle: 1993 notes on the normalized parabolic p-Laplacian
AU - Nicola Garofalo
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.13209
UR - https://arxiv.org/abs/2609.13209
AB - This note makes available, in facsimile form, a set of handwritten notes from September 1993 devoted to Bochner-type maximum principle computations for a general class of quasilinear parabolic equations which contains, as a special instance, the normalized parabolic p-Laplacian u_t = Δu + (p−2) |∇ u|^−2 ∇^2u(∇ u,∇ u). The notes were acknowledged in the introduction of the paper of Jin and Silvestre \cite{JS}, and the scheme they propose has recently been implemented in \cite{BGM} to obtain the sharp Li-Yau inequality for this equation. They are reproduced here verbatim, with no alterations, preceded by a brief introduction explaining their content and the subsequent history of the equation.
ER -