偏微分方程组的抛物型庞加莱不等式与极大函数估计
Parabolic Poincaré inequalities and maximal function estimates for systems of partial differential equations
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中文总结 AI 辅助
该研究针对非线性偏微分方程组，证明其抛物型庞加莱不等式具有自改进性，基于逐点极大函数估计推导反向赫尔德不等式与时间方向正则性结果，拓展了相关分析理论。
中文摘要 AI 辅助
我们研究非线性偏微分方程组解的抛物型庞加莱不等式，主要结果表明这些不等式具有自改进性。作为应用，我们建立了抛物柱体上平均振荡量及梯度的反向赫尔德不等式；还考虑了固定空间点处时间区间上对应的庞加莱不等式与自改进结果，这些结果基于逐点极大函数估计，进一步得到了非线性方程组解在时间方向的正则性结果。
英文摘要
We study parabolic Poincaré inequalities for solutions to nonlinear systems of partial differential equations. Our main results show that these inequalities are self-improving. As applications, we establish reverse Hölder inequalities for the mean oscillation over parabolic cylinders and for the gradient. We also consider the corresponding Poincaré inequalities and self-improvement results on time intervals at fixed spatial points. These results are based on a pointwise maximal function estimate. As an application, we obtain regularity results in the time direction for solutions to nonlinear systems.
发表机构
- Korea Institute for Advanced Study（韩国高等科学研究院）
- Aalto University（阿尔托大学）
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