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GRADIENT ESTIMATES FOR DIVERGENCE FORM ELLIPTIC SYSTEMS ARISING FROM COMPOSITE MATERIAL.
- Source :
- SIAM Journal on Mathematical Analysis; 2019, Vol. 51 Issue 3, p2444-2478, 35p
- Publication Year :
- 2019
-
Abstract
- In this paper, we show that W<superscript>1,p</superscript> (1 ≤ p < ∞ ) weak solutions to divergence form elliptic systems are Lipschitz and piecewise C¹ provided that the leading coefficients and data are of piecewise Dini mean oscillation, the lower-order coefficients are bounded, and interfacial boundaries are C<superscript>1,Dini</superscript>. This extends a result of Li and Nirenberg [Comm. Pure Appl. Math., 56 (2003), pp. 892-925]. Moreover, under a stronger assumption on the piecewise L¹-mean oscillation of the leading coefficients, we derive a global weak-type (1,1) estimate with respect to A<subscript>1</subscript> Muckenhoupt weights for the elliptic systems without lower-order terms. [ABSTRACT FROM AUTHOR]
- Subjects :
- COMPOSITE materials
ESTIMATES
OSCILLATIONS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 51
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 138378617
- Full Text :
- https://doi.org/10.1137/18M1226658