On the existence of distributional potentials

Research output: Contribution to journalResearch articleContributedpeer-review



We present proofs for the existence of distributional potentials (Formula presented.) for distributional vector fields (Formula presented.), that is, (Formula presented.), where Ω is an open subset of (Formula presented.). The hypothesis in these proofs is the compatibility condition (Formula presented.) for all (Formula presented.), if Ω is simply connected, and a stronger condition in the general case. A key tool in our treatment is the Bogovskiĭ formula, assigning vector fields (Formula presented.) satisfying (Formula presented.) to functions (Formula presented.) with (Formula presented.). The results are applied to properties of Hilbert spaces of functions occurring in the treatment of the Stokes operator and the Navier–Stokes equations.


Original languageEnglish
Pages (from-to)424-433
Number of pages10
JournalMathematische Nachrichten
Issue number1
Publication statusPublished - Jan 2023

External IDs

Scopus 85139961916
Mendeley ed942794-9b6e-35c4-aef4-3c8d7a306632


DFG Classification of Subject Areas according to Review Boards


  • Bogovskiĭ formula, Poincaré's lemma, de Rham's theorem, distribution, stokes operator

Library keywords