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

Tong Keun Chang; Hi Jun Choe

doi:10.1016/j.jmaa.2007.03.109

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

Tong Keun Chang, Hi Jun Choe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 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)} (Γ₂) and the Dirichlet data f is in H^{frac(1, 2)} (Γ₁), then the mixed boundary value problem has a unique solution and the solution is represented by potentials.

Original language	English
Pages (from-to)	794-807
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	337
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2007.03.109
Publication status	Published - 2008 Jan 15

Bibliographical note

Funding 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: tchang@ms.uky.edu, chang7357@kias.re.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2007.03.109

Cite this

@article{0ac44925f1ff4e4e868ee648e788bd8f,

title = "Mixed boundary value problem of Laplace equation in a bounded Lipschitz domain",

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) (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.",

author = "Chang, {Tong Keun} and Choe, {Hi Jun}",

note = "Funding 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: tchang@ms.uky.edu, chang7357@kias.re.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).",

year = "2008",

month = jan,

day = "15",

doi = "10.1016/j.jmaa.2007.03.109",

language = "English",

volume = "337",

pages = "794--807",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

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

AU - Chang, Tong Keun

AU - Choe, Hi Jun

N1 - Funding 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: tchang@ms.uky.edu, chang7357@kias.re.kr (T.K. Chang), choe@yonsei.ac.kr (H.J. Choe).

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

AN - SCOPUS:34548618037

SN - 0022-247X

VL - 337

SP - 794

EP - 807

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this