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The Hölder interpolative gap bound for degenerate parabolic double phase problems
Abstract
We study weak solutions to degenerate parabolic double phase equations with growth exponents 2≤ p<q and a modulating coefficient that is Hölder continuous with exponent α. If the solution itself is Hölder continuous with exponent γ, we prove higher integrability of its gradient under the gap condition q≤ p+α/(1−γ) together with q<p+1. This is the first gap bound of Hölder interpolative type for parabolic double phase problems, and it is the parabolic counterpart of the corresponding bound for elliptic problems. For α<1 it allows exponents beyond the range q≤ p+α known for bounded solutions.
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BibTeX
@misc{oh2026hölder,
title = {{The Hölder interpolative gap bound for degenerate parabolic double phase problems}},
author = {Jehan Oh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29010},
eprint = {2609.29010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29010},
}
RIS
TY - UNPB
TI - The Hölder interpolative gap bound for degenerate parabolic double phase problems
AU - Jehan Oh
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29010
UR - https://arxiv.org/abs/2609.29010
AB - We study weak solutions to degenerate parabolic double phase equations with growth exponents 2≤ p<q and a modulating coefficient that is Hölder continuous with exponent α. If the solution itself is Hölder continuous with exponent γ, we prove higher integrability of its gradient under the gap condition q≤ p+α/(1−γ) together with q<p+1. This is the first gap bound of Hölder interpolative type for parabolic double phase problems, and it is the parabolic counterpart of the corresponding bound for elliptic problems. For α<1 it allows exponents beyond the range q≤ p+α known for bounded solutions.
ER -