On the C 1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients

Yanyan Li

Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (2) : 489 -496.

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Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (2) : 489 -496. DOI: 10.1007/s11401-017-1079-4
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On the C 1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients

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Abstract

The author proves C 1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients.

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Divergence form elliptic systems / C 1 regularity / Dini-continuous coefficients

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Yanyan Li. On the C 1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients. Chinese Annals of Mathematics, Series B, 2017, 38(2): 489-496 DOI:10.1007/s11401-017-1079-4

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Brezis H.. A. Ancona: Elliptic operators, conormal derivatives and positive parts of functions, with an appendix by Haim Brezis. J. Funct. Anal., 2009, 257: 2124-2158

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Jin T. L.. Vladimir Maz’ya and Jean Van Schaftingen. Pathological solutions to elliptic problems in divergence form with continuous coefficients, C. R. Math. Acad. Sci. Paris, 2009, 347(13–14): 773-778

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Li, Y. Y., Boundary C1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients, in preparation.

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