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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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.
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
- variational problem
- operator curl
- full trace
- multiconnected domain
- semilinear degenerate system
MR Subject Classification