Title: Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity Show Chinese title

Title: 抛物型$p$-拉普拉斯方程的时间导数估计及其在最优正则性中的应用

Abstract: We establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximation method. As a consequence, we obtain an optimal regularity result with a connection to the well-known $C^{p'}$-conjecture in the elliptic setting. Finally, we extend our method to treat global regularity results for both fully nonlinear and general quasilinear degenerate parabolic problems. Show Chinese abstract

Abstract: 我们建立了抛物型$p$-拉普拉斯方程解的时间导数的有界性。 我们的方法依赖于伯恩斯坦技巧结合一种合适的逼近方法。 作为结果，我们得到了一个与椭圆情形中众所周知的$C^{p'}$-猜想有关的最佳正则性结果。 最后，我们将该方法扩展以处理完全非线性和一般拟线性退化抛物问题的全局正则性结果。