发表机构
Kyungpook National University（庆北国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对退化抛物双相方程，在解具有Hölder连续性时，提出并证明了满足间隙条件$q\le p+\alpha/(1-\gamma)$的梯度更高可积性，首次给出Hölder插值型间隙界。
AI 中文摘要
我们研究增长指数为$2\le p<q$且调制系数具有指数$\alpha$的Hölder连续性的退化抛物双相方程的弱解。如果解本身具有指数$\gamma$的Hölder连续性，我们在间隙条件$q\le p+\alpha/(1-\gamma)$以及$q<p+1$下证明其梯度的更高可积性。这是抛物双相问题中第一个Hölder插值型间隙界，并且是椭圆问题相应界的抛物对应。对于$\alpha<1$，它允许指数超出已知有界解的范围$q\le p+\alpha$。
英文摘要
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.
