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

Tong Keun Chang, Hi Jun Choe

Research output: Contribution to journalArticle

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

Fingerprint

Lipschitz Domains
Mixed Boundary Value Problem
Laplace equation
Laplace's equation
Boundary value problems
Bounded Domain
Unique Solution
Dirichlet
Existence and Uniqueness

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain. / Chang, Tong Keun; Choe, Hi Jun.

In: Journal of Mathematical Analysis and Applications, Vol. 337, No. 2, 15.01.2008, p. 794-807.

Research output: Contribution to journalArticle

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AU - Choe, Hi Jun

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AB - 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) (Γ2) and the Dirichlet data f is in Hfrac(1, 2) (Γ1), then the mixed boundary value problem has a unique solution and the solution is represented by potentials.

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