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Mean oscillation gradient estimates for elliptic systems in divergence form with VMO coefficients

Abstract:

We consider gradient estimates for H1 solutions of linear elliptic systems in divergence form ∂α(Aαβij∂βuj)=0. It is known that the Dini continuity of coefficient matrix A=(Aαβij) is essential for the differentiability of solutions. We prove the following results: (a) If A satisfies a condition slightly weaker than Dini continuity but stronger than belonging to VMO, namely that the L2 mean oscillation ωA,2 of A satisfies $ X_{A,2} := \limsup\limits_{r\rightarrow 0} r {{\int \limits }_{r}^{2...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s40306-022-00493-y

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer
Journal:
Acta Mathematica Vietnamica More from this journal
Volume:
48
Pages:
117-132
Publication date:
2023-02-02
Acceptance date:
2022-12-05
DOI:
ISSN:
0251-4184
Language:
English
Keywords:
Pubs id:
1315342
Local pid:
pubs:1315342
Deposit date:
2022-12-16

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