Minimizers of curl prescribed full trace
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.
关键词：
variational problem,
operator curl,
full trace, multiconnected domain,
semilinear degenerate system
