Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets

Yuanyuan Lian

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arXiv · 2405.07214

Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets

Yuanyuan Lian

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Abstract

In this paper, we obtain the interior pointwise $C^{k,\alpha}$ ($k\geq 0$, $0<\alpha<1$) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions.

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Yuanyuan Lian. 2024-05-12. Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets. https://arxiv.org/abs/2405.07214

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