no. 1
Uniform bounds for quotients of Green functions on C 1,1 -domains
Annales de l'Institut Fourier, Tome 32 (1982) no. 1, pp. 105-117.

Soient Δu=Σ i ∂ 2 ∂ x i 2 , Lu=Σ i,j a ij ∂ 2 ∂x i ∂x j u+Σ i b i ∂ ∂x i u+cu des opérateurs elliptiques à coefficients höldériens sur un domaine borné Ω⊂R n de classe C 1,1 . Il existe une constante c>0 ne dépendant que des normes de Hölder des coefficients de L et de sa constante d’ellipticité telle que

c-1GΔΩ≤GLΩ≤cGΔΩsurΩ×Ω,

γ Δ Ω (resp. G L Ω ) étant la fonction de Green de Δ (resp. L) sur Ω.

Let Δu=Σ i ∂ 2 ∂ x i 2 , Lu=Σ i,j a ij ∂ 2 ∂x i ∂x j u+Σ i b i ∂ ∂x i u+cu be elliptic operators with Hölder continuous coefficients on a bounded domain Ω⊂R n of class C 1,1 . There is a constant c>0 depending only on the Hölder norms of the coefficients of L and its constant of ellipticity such that

c-1GΔΩ≤GLΩ≤cGΔΩonΩ×Ω,

where γ Δ Ω (resp. G L Ω ) are the Green functions of Δ (resp. L) on Ω.

@article{AIF_1982__32_1_105_0,
     author = {Hueber, H. and Sieveking, M.},
     title = {Uniform bounds for quotients of {Green} functions on $C^{1,1}$-domains},
     journal = {Annales de l'Institut Fourier},
     pages = {105--117},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {1},
     year = {1982},
     doi = {10.5802/aif.861},
     zbl = {0465.35028},
     mrnumber = {84a:35063},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.861/}
}
TY  - JOUR
AU  - Hueber, H.
AU  - Sieveking, M.
TI  - Uniform bounds for quotients of Green functions on $C^{1,1}$-domains
JO  - Annales de l'Institut Fourier
PY  - 1982
SP  - 105
EP  - 117
VL  - 32
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.861/
DO  - 10.5802/aif.861
LA  - en
ID  - AIF_1982__32_1_105_0
ER  - 
%0 Journal Article
%A Hueber, H.
%A Sieveking, M.
%T Uniform bounds for quotients of Green functions on $C^{1,1}$-domains
%J Annales de l'Institut Fourier
%D 1982
%P 105-117
%V 32
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.861/
%R 10.5802/aif.861
%G en
%F AIF_1982__32_1_105_0
Hueber, H.; Sieveking, M. Uniform bounds for quotients of Green functions on $C^{1,1}$-domains. Annales de l'Institut Fourier, Tome 32 (1982) no. 1, pp. 105-117. doi : 10.5802/aif.861. https://aif.centre-mersenne.org/articles/10.5802/aif.861/

[1] A. Ancona, Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine Lipschitzien, Ann. Inst. Fourier, 28, 4 (1978), 169-213. | Numdam | MR | Zbl

[2] A. Ancona, Principe de Harnack à la frontière et problèmes de frontière de Martin, Lecture Notes in Mathematics, 787 (1980), 9-28. | MR | Zbl

[3] N. Boboc, P. Mustata, Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique, Lecture Notes in Mathematics, 68 (1968). | MR | Zbl

[4] C. Constantinescu, A. Cornea, Potential theory on harmonic spaces, Berlin-Heidelberg-New York, 1972. | MR | Zbl

[5] D. Gilbarg, J. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. d'Anal. Math., 4 (1954-1956), 309-340. | MR | Zbl

[6] R.M. Herve, Recherches axiomatiques sur la théorie des fonctions surhamoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. | Numdam | MR | Zbl

[7] H. Hueber, M. Sieveking, On the quotients of Green functions (preliminary version), Bielefeld, September 1980 (unpublished).

[8] J. Serrin, On the Harnack inequality for linear elliptic equations, J. d'Anal. Math., 4 (1956), 292-308. | MR | Zbl

[9] J.-C. Taylor, On the Martin compactification of a bounded Lipschitz domain in a Riemannian manifold, Ann. Inst. Fourier, 28, 2 (1977), 25-52. | Numdam | MR | Zbl

Cité par Sources :