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arXiv · 2311.06846

Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients

Hongjie Dong·Seongmin Jeon·Stefano Vita
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Abstract

In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^\alpha A\nabla u)=\text{div}(x_n^\alpha \mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $\alpha>-1$, we establish boundary Schauder type estimates under the conormal boundary condition on the flat boundary, provided that the coefficients satisfy Dini mean oscillation (DMO) type conditions. Additionally, as an application, we derive higher-order boundary Harnack principles for uniformly elliptic equations in divergence form with DMO coefficients.

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Hongjie Dong, Seongmin Jeon, Stefano Vita. 2023-11-12. Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients. https://doi.org/10.1007/s00526-024-02840-3

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