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arXiv · 2412.00675

H\"older regularity of solutions of degenerate parabolic equations of general dimension

Hyo Seok Jang·Ki-Ahm Lee
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Abstract

We establish the Alexandroff-Bakelman-Pucci estimate, the Harnack inequality, the H\"older regularity and the Schauder estimates to a class of degenerate parabolic equations of non-divergence form in all dimensions \begin{equation} \mathcal{L}u:= u_t -Lu= u_t -(x a_{11} u_{xx} +2\sqrt{x} \sum_{j=2}^n a_{1j} u_{x y_j} + \sum_{i,j=2}^n a_{ij} u_{y_i y_j} + b_1 u_x +\sum_{j=2}^n b_j u_{y_j} ) =g\ \end{equation} on \(x \geq 0, y=(y_2,\ldots, y_n) \in \mathbb{R}^{n-1}\), with bounded measurable coefficients.

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Hyo Seok Jang, Ki-Ahm Lee. 2024-12-01. H\"older regularity of solutions of degenerate parabolic equations of general dimension. https://arxiv.org/abs/2412.00675

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