Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain

Tong Keun Chang, Hi Jun Choe

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4 Citations (Scopus)

Abstract

We study the existence and uniqueness of the mixed boundary value problem for Laplace equation in a bounded Lipschitz domain Ω ⊂ Rn, n ≥ 3. Let the boundary ∂Ω of Ω be decomposed by ∂ Ω = Γ = Γ1 ∪ over(Γ, -)2 = over(Γ, -)1 ∪ Γ2, Γ1 ∩ Γ2 = ∅. We will show that if the Neumann data ψ is in H- frac(1, 2)2) and the Dirichlet data f is in Hfrac(1, 2)1), then the mixed boundary value problem has a unique solution and the solution is represented by potentials.

Original languageEnglish
Pages (from-to)794-807
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume337
Issue number2
DOIs
Publication statusPublished - 2008 Jan 15

Bibliographical note

Funding Information:
✩ The first author is supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) KRF-2005-214-C00179. The second author is partially supported by KERI and the Korea Research Foundation Grant KRF C-00005. * Corresponding author. Present address: School of Mathematics, Korea Institute for Advanced Study, Republic of Korea. E-mail addresses: tchang@ms.uky.edu, chang7357@kias.re.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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