• Corpus ID: 119323345

Representation of vector fields

@inproceedings{AGRamm2015RepresentationOV,
  title={Representation of vector fields},
  author={A.G.Ramm},
  year={2015}
}

• A.G.Ramm
• Published 2 March 2015
• Mathematics

A simple proof is given for the explicit formula which allows one to recover a C2−smooth vector field A = A(x) in R3, decaying at infinity, from the knowledge of its ∇×A and ∇ ·A. The representation of A as a sum of the gradient field and a divergence-free vector fields is derived from this formula. Similar results are obtained for a vector field in a bounded C2−smooth domain. Mathematics Subject Classification: MSC 2010, 26B99, 76D99, 78A99