Remark on the Helmholtz decomposition in domains with noncompact boundary

Yasunori Maekawa, Hideyuki Miura

研究成果: Article査読

10 被引用数 (Scopus)

抄録

Let Ω be a domain in ℝd+1 whose boundary is given as a uniform Lipschitz graph xd+1=η(x) for x ∈ ℝd. For such a domain, it is known that the Helmholtz decomposition is not always valid in Lp(Ω) except for the energy space L2(Ω). In this paper we show that the Helmholtz decomposition still holds in certain anisotropic spaces which include vector fields decaying slowly in the xd+1 variable. In particular, these classes include some infinite energy vector fields. For the purpose, we develop a new approach based on a factorization of divergence form elliptic operators whose coefficients are independent of one variable.

本文言語English
ページ(範囲)1077-1095
ページ数19
ジャーナルMathematische Annalen
359
3-4
DOI
出版ステータスPublished - 2014 8

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「Remark on the Helmholtz decomposition in domains with noncompact boundary」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル