AI 中文总结
研究具p增长与非散度数据的非线性抛物系统，提出不要求向量场梯度可微的方法，统一处理奇异与退化情形，建立解梯度的局部更高可积性估计。
AI 中文摘要
我们获得了具多项式p增长且右端为非散度形式的非线性抛物系统弱解的Calderón-Zygmund估计。我们的方法不要求向量场关于梯度变量可微，且能统一处理奇异与退化两种情形。特别地，我们根据右端的可积性依赖关系，建立了解的梯度的局部更高可积性估计。
英文摘要
We obtain Calderón--Zygmund estimates for weak solutions to nonlinear parabolic systems with polynomial $p$-growth and the right-hand side in non-divergence form. Our approach does not require differentiability of the vector field with respect to the gradient variable and provides a unified treatment of both the singular and degenerate regimes. In particular, we establish local higher-integrability estimates for the gradient of the solution under appropriate dependency on the integrability of the right-hand side.
Comments25 pages
