Hessian Estimates for Non-divergence form Elliptic Equations Arising from Composite Materials

被引：2
|
作者：
Dong, Hongjie [1 ]
Xu, Longjuan [2 ]
机构：
[1] Brown Univ, Div Appl Math, 182 George St, Providence, RI 02912 USA
[2] Yonsei Univ, Dept Math, 50 Yonsei Ro, Seoul 03722, South Korea
来源：
POTENTIAL ANALYSIS | 2021年 / 54卷 / 03期
关键词：
Non-divergence form elliptic equations; Adjoint solutions; Piecewise DMO coefficients; Hessian estimates; Weak-type (1,1) estimates; NONDIVERGENCE FORM; REGULARITY; SYSTEMS; OPERATORS; BOUNDARY; C-1;
D O I：
10.1007/s11118-020-09832-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove that any W-2,W-1 strong solution to second-order non-divergence form elliptic equations is locally W-2,W-infinity and piecewise C-2 when the leading coefficients and data are of piecewise Dini mean oscillation and the lower-order terms are bounded. Somewhat surprisingly here the interfacial boundaries are only required to be in C-1,C-Dini. We also derive global weak-type (1,1) estimates with respect to A(1) Muckenhoupt weights. The corresponding results for the adjoint operator are established. Our estimates are independent of the distance between these surfaces of discontinuity of the coefficients
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页码：409 / 449
页数：41
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