Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain |
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| Authors: | TongKeun Chang Hi Jun Choe |
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| Affiliation: | a Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA
b Department of Mathematics, Yonsei University, Seoul, South Korea |
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| 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  , Γ1∩Γ2=∅. We will show that if the Neumann data ψ is in  and the Dirichlet data f is in  , then the mixed boundary value problem has a unique solution and the solution is represented by potentials. |
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| Keywords: | Mixed boundary value problem Bounded Lipschitz domain Single layer potential Double layer potential |
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