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

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.

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.

@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},
     year = {1982},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {1},
     doi = {10.5802/aif.861},
     zbl = {0465.35028},
     mrnumber = {84a:35063},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.861/}
}
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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

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