The mixed problem for the Lamé system in a class of Lipschitz domains

Russell M. Brown; Irina Mitrea

doi:10.1016/j.jde.2009.01.008

The mixed problem for the Lamé system in a class of Lipschitz domains

Russell M. Brown
, Irina Mitrea

Mathematics

Producción científica: Article › revisión exhaustiva

29 Citas (Scopus)

Resumen

We consider the mixed problem for the Lamé system{(L u = 0, in Ω,; u |_D = f_D, on D,; frac(∂ u, ∂ ρ) = f_N, on N,; (∇ u)^* ∈ L^p (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data f_D has one derivative in L^p (D) and the traction data f_N is in L^p (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in L^p (∂ Ω).

Idioma original	English
Páginas (desde-hasta)	2577-2589
Número de páginas	13
Publicación	Journal of Differential Equations
Volumen	246
N.º	7
DOI	https://doi.org/10.1016/j.jde.2009.01.008
Estado	Published - abr 1 2009

Nota bibliográfica

Funding Information:
✩ Research supported in part by the NSF DMS Grant 0547944.

Financiación

\u2729 Research supported in part by the NSF DMS Grant 0547944.

Financiadores	Número del financiador
NSF CAREER DMS-1149054
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	0547944
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2009.01.008

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@article{fc47a4c6b6e74d85aaa534c8bf62272d,

title = "The mixed problem for the Lam{\'e} system in a class of Lipschitz domains",

abstract = "We consider the mixed problem for the Lam{\'e} system\{(L u = 0, in Ω,; u |D = fD, on D,; frac(∂ u, ∂ ρ) = fN, on N,; (∇ u)* ∈ Lp (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data fD has one derivative in Lp (D) and the traction data fN is in Lp (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in Lp (∂ Ω).",

keywords = "Lam{\'e} system, Layer potentials, Lipschitz domains, Mixed boundary value problems, Well-posedness",

author = "Brown, \{Russell M.\} and Irina Mitrea",

note = "Funding Information: ✩ Research supported in part by the NSF DMS Grant 0547944.",

year = "2009",

month = apr,

day = "1",

doi = "10.1016/j.jde.2009.01.008",

language = "English",

volume = "246",

pages = "2577--2589",

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T1 - The mixed problem for the Lamé system in a class of Lipschitz domains

AU - Brown, Russell M.

AU - Mitrea, Irina

N1 - Funding Information: ✩ Research supported in part by the NSF DMS Grant 0547944.

PY - 2009/4/1

Y1 - 2009/4/1

N2 - We consider the mixed problem for the Lamé system{(L u = 0, in Ω,; u |D = fD, on D,; frac(∂ u, ∂ ρ) = fN, on N,; (∇ u)* ∈ Lp (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data fD has one derivative in Lp (D) and the traction data fN is in Lp (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in Lp (∂ Ω).

AB - We consider the mixed problem for the Lamé system{(L u = 0, in Ω,; u |D = fD, on D,; frac(∂ u, ∂ ρ) = fN, on N,; (∇ u)* ∈ Lp (∂ Ω)) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω and ∂ / ∂ ρ stands for the traction operator. We suppose the Dirichlet data fD has one derivative in Lp (D) and the traction data fN is in Lp (N). For p in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in Lp (∂ Ω).

KW - Lamé system

KW - Layer potentials

KW - Lipschitz domains

KW - Mixed boundary value problems

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/60349129659

UR - https://www.scopus.com/pages/publications/60349129659#tab=citedBy

U2 - 10.1016/j.jde.2009.01.008

DO - 10.1016/j.jde.2009.01.008

M3 - Article

AN - SCOPUS:60349129659

SN - 0022-0396

VL - 246

SP - 2577

EP - 2589

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 7

ER -

The mixed problem for the Lamé system in a class of Lipschitz domains

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Nota bibliográfica

Financiación

ASJC Scopus subject areas

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