The Hölder interpolative gap bound for degenerate parabolic double phase problems

Jehan Oh

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arXiv · 2609.29010

The Hölder interpolative gap bound for degenerate parabolic double phase problems

Jehan Oh

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Abstract

We study weak solutions to degenerate parabolic double phase equations with growth exponents $2\le p<q$ 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 $q\le p+α/(1-γ)$ 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 $q\le p+α$ known for bounded solutions.

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Jehan Oh. 2026-09-24. The Hölder interpolative gap bound for degenerate parabolic double phase problems. https://arxiv.org/abs/2609.29010

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