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Gradient estimates for elliptic systems in non-smooth domains

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Abstract

We obtain the global W 1,p, 1  <  p  < ∞, estimate for the weak solution of an elliptic system with discontinuous coefficients in non-smooth domains without using maximal function approach. It is assumed that the boundary of a bounded domain is well approximated by hyperplanes at every point and at every scale, and that the tensor coefficients belong to BMO space with their BMO semi-norms sufficiently small.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, South Korea

    Sun-Sig Byun

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Lihe Wang

  3. College of Sciences, Xian Jiaotong University, Xian, 710049, China

    Lihe Wang

Authors
  1. Sun-Sig Byun
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  2. Lihe Wang
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Corresponding author

Correspondence to Sun-Sig Byun.

Additional information

S.-S. Byun was supported in part by KRF-2006-C00034 and L. Wang was supported in part by NSF Grant 0701392.

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Byun, SS., Wang, L. Gradient estimates for elliptic systems in non-smooth domains. Math. Ann. 341, 629–650 (2008). https://doi.org/10.1007/s00208-008-0207-6

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  • DOI: https://doi.org/10.1007/s00208-008-0207-6

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