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.
Bibliographical noteFunding 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: firstname.lastname@example.org, email@example.com (T.K. Chang), firstname.lastname@example.org (H.J. Choe).
All Science Journal Classification (ASJC) codes
- Applied Mathematics