Coercive energy estimates for differential forms in semi-convex domains

Dorina Mitrea*, Irina Mitrea, Marius Mitrea, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)

    Abstract

    In this paper, we prove a H1-coercive estimate for differential forms of arbitrary degrees in semi-convex domains of the Euclidean space. The key result is an integral identity involving a boundary term in which the Weingarten matrix of the boundary intervenes, established for any Lipschitz domain Ω⊆ℝnwhose outward unit normal v belongs to Ln-11(∂Ω), the Ln-1-based Sobolev space of order one on ∂Ω.

    Original languageEnglish
    Pages (from-to)987-1010
    Number of pages24
    JournalCommunications on Pure and Applied Analysis
    Volume9
    Issue number4
    DOIs
    Publication statusPublished - Jul 2010

    Keywords

    • Coercive estimates
    • Differential forms
    • Semi-convex domains
    • Weingarten map

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