Square function estimates for the evolutionary p-Laplace equation

Kaj Nyström

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arXiv · 2209.06705

Square function estimates for the evolutionary p-Laplace equation

Kaj Nyström

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Abstract

We prove novel (local) square function/Carleson measure estimates for non-negative solutions to the evolutionary $p$-Laplace equation in the complement of parabolic Ahlfors-David regular sets. In the case of the heat equation, the Laplace equation as well as the $p$-Laplace equation, the corresponding square function estimates have proven fundamental in symmetry and inverse/free boundary type problems, and in particular in the study of (parabolic) uniform rectifiability. Though the implications of the square function estimates are less clear for the evolutionary $p$-Laplace equation, mainly due its lack of homogeneity, we give some initial applications to parabolic uniform rectifiability, boundary behaviour and Fatou type theorems for $\nabla_Xu$.

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Kaj Nyström. 2022-09-14. Square function estimates for the evolutionary p-Laplace equation. https://arxiv.org/abs/2209.06705

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