English

Laplace invariants of differential operators

Mathematical Physics 2020-12-22 v3 math.MP

Abstract

We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential invariants of partial differential operators under gauge transformations and introduce a sufficient condition for a set of invariants to be complete. We also give a some mild conditions that guarantee the existence of such a set. The proof is constructive. The method gives many examples of invariants previously known in the literature as well as many new examples including multidimensional.

Keywords

Cite

@article{arxiv.2003.03467,
  title  = {Laplace invariants of differential operators},
  author = {David Hobby and Ekaterina Shemyakova},
  journal= {arXiv preprint arXiv:2003.03467},
  year   = {2020}
}
R2 v1 2026-06-23T14:07:09.152Z