Schauder estimates for quasilinear parabolic equations with general Orlicz growth
Abstract
We develop a unified approach to Schauder estimates for scalar parabolic equations ∂t u−div(𝒜(x,t,Du))=f(x,t) with general Orlicz growth and coefficients that are Hölder continuous in the spatial variables and merely measurable in time. Combining intrinsic gradient estimates with a perturbative argument, we establish quantitative local bounds and Hölder estimates for the spatial gradient in the supercritical range and, for locally bounded weak solutions, throughout the full admissible growth range. Our results extend the Schauder regularity theory for parabolic p-Laplace type equations to a broad class of possibly nonradial operators with Orlicz growth, while simplifying the regularity arguments and treating singular, degenerate, and mixed growth laws within a unified framework.
Related
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BibTeX
@misc{antonini2026schauder,
title = {{Schauder estimates for quasilinear parabolic equations with general Orlicz growth}},
author = {Carlo Alberto Antonini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27426},
eprint = {2610.27426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27426},
}
RIS
TY - UNPB
TI - Schauder estimates for quasilinear parabolic equations with general Orlicz growth
AU - Carlo Alberto Antonini
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27426
UR - https://arxiv.org/abs/2610.27426
AB - We develop a unified approach to Schauder estimates for scalar parabolic equations ∂_t u−div(𝒜(x,t,Du))=f(x,t) with general Orlicz growth and coefficients that are Hölder continuous in the spatial variables and merely measurable in time. Combining intrinsic gradient estimates with a perturbative argument, we establish quantitative local bounds and Hölder estimates for the spatial gradient in the supercritical range and, for locally bounded weak solutions, throughout the full admissible growth range. Our results extend the Schauder regularity theory for parabolic p-Laplace type equations to a broad class of possibly nonradial operators with Orlicz growth, while simplifying the regularity arguments and treating singular, degenerate, and mixed growth laws within a unified framework.
ER -