PreprintCC BY 4.0arXiv
Time derivative estimates for normalized parabolic p-Laplace equations
Abstract
We establish the local boundedness of time derivatives of bounded viscosity solutions to the normalized parabolic p-Laplace equation for every p∈(1,∞). The proof combines a logarithmic Bernstein argument with quantitative stability to derive a recursive estimate between different regularizations. For p=1 and n≥2, we construct a bounded viscosity solution which is not Hölder continuous in time with any positive exponent.
Related
- Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations
- Normalized solutions to 1-Laplace equations with critical growth term
- Local behavior of solutions to inhomogeneous singular parabolic p-Laplace equations
- Harnack Inequality for Parabolic Fractional p-Laplace Equations
- Regularity for solutions to inhomogeneous degenerate parabolic p-Laplace equations
BibTeX
@misc{lee2026time,
title = {{Time derivative estimates for normalized parabolic $p$-Laplace equations}},
author = {Se-Chan Lee and Hyungsung Yun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15501},
eprint = {2609.15501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time derivative estimates for normalized parabolic p-Laplace equations
AU - Se-Chan Lee
AU - Hyungsung Yun
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15501
UR - https://arxiv.org/abs/2609.15501
AB - We establish the local boundedness of time derivatives of bounded viscosity solutions to the normalized parabolic p-Laplace equation for every p∈(1,∞). The proof combines a logarithmic Bernstein argument with quantitative stability to derive a recursive estimate between different regularizations. For p=1 and n≥2, we construct a bounded viscosity solution which is not Hölder continuous in time with any positive exponent.
ER -