Expansion de la fonction de Green pour les opérateurs de type divergence

Saïma Khenissy; Yomna Rébaï; Dong Ye

doi:10.1016/j.crma.2010.06.024

Expansion de la fonction de Green pour les opérateurs de type divergence

Saïma Khenissy^*
, Yomna Rébaï
, Dong Ye

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

We consider the fundamental solution Ga of the operator -Δ_a=-1/a(x)div(a(x)▽·) on a bounded smooth domain Ω⊂Rⁿ (n≥2), associated to the Dirichlet boundary condition, where a is a positive smooth function on Ω. In this short Note, we give a precise description of the function Ga(x,y). In particular, we define in a unique way its continuous part Ha(x,y) and we prove that the corresponding Robin's function Ra(x)=Ha(x,x) belongs to C^∞(Ω), although H_a∉C¹(Ω×Ω) in general.

投稿的翻译标题	Expansion of the Green's function for divergence form operators
源语言	法语
页（从-至）	891-896
页数	6
期刊	Comptes Rendus Mathematique
卷	348
期	15-16
DOI	https://doi.org/10.1016/j.crma.2010.06.024
出版状态	已出版 - 8月 2010
已对外发布	是

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abstract = "We consider the fundamental solution Ga of the operator -Δa=-1/a(x)div(a(x)▽·) on a bounded smooth domain Ω⊂Rn (n≥2), associated to the Dirichlet boundary condition, where a is a positive smooth function on Ω. In this short Note, we give a precise description of the function Ga(x,y). In particular, we define in a unique way its continuous part Ha(x,y) and we prove that the corresponding Robin's function Ra(x)=Ha(x,x) belongs to C∞(Ω), although Ha∉C1(Ω×Ω) in general.",

author = "Sa{\"i}ma Khenissy and Yomna R{\'e}ba{\"i} and Dong Ye",

year = "2010",

month = aug,

doi = "10.1016/j.crma.2010.06.024",

language = "法语",

volume = "348",

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journal = "Comptes Rendus Mathematique",

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T1 - Expansion de la fonction de Green pour les opérateurs de type divergence

AU - Khenissy, Saïma

AU - Rébaï, Yomna

AU - Ye, Dong

PY - 2010/8

Y1 - 2010/8

N2 - We consider the fundamental solution Ga of the operator -Δa=-1/a(x)div(a(x)▽·) on a bounded smooth domain Ω⊂Rn (n≥2), associated to the Dirichlet boundary condition, where a is a positive smooth function on Ω. In this short Note, we give a precise description of the function Ga(x,y). In particular, we define in a unique way its continuous part Ha(x,y) and we prove that the corresponding Robin's function Ra(x)=Ha(x,x) belongs to C∞(Ω), although Ha∉C1(Ω×Ω) in general.

AB - We consider the fundamental solution Ga of the operator -Δa=-1/a(x)div(a(x)▽·) on a bounded smooth domain Ω⊂Rn (n≥2), associated to the Dirichlet boundary condition, where a is a positive smooth function on Ω. In this short Note, we give a precise description of the function Ga(x,y). In particular, we define in a unique way its continuous part Ha(x,y) and we prove that the corresponding Robin's function Ra(x)=Ha(x,x) belongs to C∞(Ω), although Ha∉C1(Ω×Ω) in general.

UR - https://www.scopus.com/pages/publications/77955770369

U2 - 10.1016/j.crma.2010.06.024

DO - 10.1016/j.crma.2010.06.024

M3 - 文章

AN - SCOPUS:77955770369

SN - 1631-073X

VL - 348

SP - 891

EP - 896

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 15-16

ER -

Expansion de la fonction de Green pour les opérateurs de type divergence

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