The Neumann problem and Helmholtz decomposition in convex domains

Jun Geng, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We show that the Neumann problem for Laplace's equation in a convex domain ω with boundary data in Lp(∂ω) is uniquely solvable for 1 < p < ∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(ω,Rd).

Original languageEnglish
Pages (from-to)2147-2164
Number of pages18
JournalJournal of Functional Analysis
Issue number8
StatePublished - Oct 2010

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (J. Geng), [email protected] (Z. Shen). 1 Supported in part by NSF grant DMS-0855294.


  • Convex domains
  • Helmholtz decomposition
  • Neumann problem

ASJC Scopus subject areas

  • Analysis


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