Minimizers of curl prescribed full trace

Abstract

This paper concerns the minimization problem of L2 norm of curl of vector fields prescribed full trace on the boundary of a multiconnected bounded domain. The existence of the minimizers in H1 are shown by orthogonal decompositions of vector function spaces and a constructed auxiliary variational problem. And the H2 estimate of the type II divergence-free part of the minimizers is established by div-curl-gradient type estimates of vector fields.

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Acknowledgements

The author is grateful to her supervisor, Professor Xing-Bin Pan, for guidance and constant encouragement. And the referees are thanked for the valuable comments which helped to improve this article.

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Correspondence to Jun Chen.

Additional information

Supported by the National Natural Science Foundation of China (11501109) and Designated Scientific Research Project of Provincial Universities of Fujian Province (JK2015014).

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Chen, J. Minimizers of curl prescribed full trace. Appl. Math. J. Chin. Univ. 35, 157–165 (2020). https://doi.org/10.1007/s11766-020-3633-1

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Keywords

  • variational problem
  • operator curl
  • full trace
  • multiconnected domain
  • semilinear degenerate system

MR Subject Classification

  • 35Q60
  • 35J50
  • 35J57