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Regularity Results for the Generalized Beltrami System

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Abstract

For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class \( W^{{1,r}}_{{{\text{loc}}}} {\left( {\Omega ,\mathbb{R}^{n} } \right)} \) (1 < r < n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved.

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Authors and Affiliations

  1. Department of Mathematics, Northern Jiaotong University, Beijing, 100044, P. R. China

    Shen Zhou Zheng

  2. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Shen Zhou Zheng

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  1. Shen Zhou Zheng
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Correspondence to Shen Zhou Zheng.

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Supported by the National Natural Science Foundation of China (49805005) and by the research foundation of Northern Jiaotong University (2002SM061)

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Zheng, S.Z. Regularity Results for the Generalized Beltrami System. Acta Math Sinica 20, 293–304 (2004). https://doi.org/10.1007/s10114-003-0250-x

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  • DOI: https://doi.org/10.1007/s10114-003-0250-x

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