### Abstract

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

Original language | English |
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Pages (from-to) | 794-807 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 337 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Jan 15 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 337, no. 2, pp. 794-807. https://doi.org/10.1016/j.jmaa.2007.03.109

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain

AU - Chang, Tong Keun

AU - Choe, Hi Jun

PY - 2008/1/15

Y1 - 2008/1/15

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34548618037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548618037&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2007.03.109

DO - 10.1016/j.jmaa.2007.03.109

M3 - Article

VL - 337

SP - 794

EP - 807

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -