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arXiv · 2503.04384

Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity

Se-Chan Lee·Yuanyuan Lian·Hyungsung Yun·Kai Zhang
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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.

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Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun, Kai Zhang. 2025-03-06. Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity. https://arxiv.org/abs/2503.04384

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