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

Fuente: arXiv
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Main Authors: Dong, Hongjie, Jeon, Seongmin, Vita, Stefano
Format: Preprint
Published: 2023
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_version_ 1866913573883609088
author Dong, Hongjie
Jeon, Seongmin
Vita, Stefano
author_facet Dong, Hongjie
Jeon, Seongmin
Vita, Stefano
contents In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^αA\nabla u)=\text{div}(x_n^α\mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $α>-1$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_06846
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
Dong, Hongjie
Jeon, Seongmin
Vita, Stefano
Analysis of PDEs
35B45, 35B65, 35J70, 35J75
In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^αA\nabla u)=\text{div}(x_n^α\mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $α>-1$, 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.
title Schauder type estimates for degenerate or singular elliptic equations with DMO coefficients
topic Analysis of PDEs
35B45, 35B65, 35J70, 35J75
url https://arxiv.org/abs/2311.06846