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

Translated title of the contribution: Expansion of the Green's function for divergence form operators

Saïma Khenissy, Yomna Rébaï, Dong Ye

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

6 Scopus citations

Abstract

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.

Translated title of the contribution	Expansion of the Green's function for divergence form operators
Original language	French
Pages (from-to)	891-896
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	15-16
DOIs	https://doi.org/10.1016/j.crma.2010.06.024
State	Published - Aug 2010
Externally published	Yes

Access to Document

10.1016/j.crma.2010.06.024

Cite this

@article{9d3a00ccc90b451c8a1890114fe90ba3,

title = "Expansion de la fonction de Green pour les op{\'e}rateurs de type divergence",

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",

pages = "891--896",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Academie des sciences",

number = "15-16",

}

TY - JOUR

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this