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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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References

  1. Brezis, H., On a conjecture of J. Serrin, Rend. Lincei Mat. Appl., 19, 2008, 335–338.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. 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, 347(13–14), 2009, 773–778.

    Google Scholar 

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

  5. Li, Y. Y. and Nirenberg, L., Estimates for elliptic systems from composite material, Comm. Pure Appl. Math., 56, 2003, 892–925.

    Article  MathSciNet  MATH  Google Scholar 

  6. Lieberman, G., Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions, Ann. Mat. Pura Appl., 148, 1987, 77–99.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA

    Yanyan Li

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  1. Yanyan Li
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Correspondence to Yanyan Li.

Additional information

Dedicated to Haim Brezis on his 70th birthday with friendship and admiration

The work is partially supported by NSF grants DMS-1065971 and DMS-1501004.

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Li, Y. On the C 1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients. Chin. Ann. Math. Ser. B 38, 489–496 (2017). https://doi.org/10.1007/s11401-017-1079-4

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  • DOI: https://doi.org/10.1007/s11401-017-1079-4

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