### 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