Remark on the Helmholtz decomposition in domains with noncompact boundary

2013/07/30 by Yasunori Maekawa, Maekawa, Yasunori, Hideyuki Miura +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1307.8168

openalex publication_date 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a domain with noncompact boundary. It is known that the Helmholtz decomposition is not always valid in L^p(Ω) except for the energy space L² (Ω). In this paper we consider a typical unbounded domain whose boundary is given as a Lipschitz graph, and show that the Helmholtz decomposition holds in certain anisotropic spaces which include some infinite energy vector fields.

Citations

• A New Approach to Absolute Continuity of Elliptic Measure, with Applications to Non-symmetric Equations

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