Boundary estimates for elliptic operators in divergence form with VMO coefficients

Hongjie Dong; Seongmin Jeon

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arXiv · 2502.02755

Boundary estimates for elliptic operators in divergence form with VMO coefficients

Hongjie Dong·Seongmin Jeon

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Abstract

We establish boundary regularity estimates for elliptic systems in divergence form with VMO coefficients. Additionally, we obtain nondegeneracy estimates of the Hopf-Oleinik type lemma for elliptic equations. In both cases, the moduli of continuity are expressed in terms of the $L^p$-mean oscillations of the coefficients and data.

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Hongjie Dong, Seongmin Jeon. 2025-02-04. Boundary estimates for elliptic operators in divergence form with VMO coefficients. https://arxiv.org/abs/2502.02755

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