Let , be elliptic operators with Hölder continuous coefficients on a bounded domain of class . There is a constant depending only on the Hölder norms of the coefficients of and its constant of ellipticity such that
where (resp. ) are the Green functions of (resp. ) on .
Soient , des opérateurs elliptiques à coefficients höldériens sur un domaine borné de classe . Il existe une constante ne dépendant que des normes de Hölder des coefficients de et de sa constante d’ellipticité telle que
(resp. ) étant la fonction de Green de (resp. ) sur .
@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, Volume 32 (1982) no. 1, pp. 105-117. doi : 10.5802/aif.861. https://aif.centre-mersenne.org/articles/10.5802/aif.861/
[1] 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] Principe de Harnack à la frontière et problèmes de frontière de Martin, Lecture Notes in Mathematics, 787 (1980), 9-28. | MR | Zbl
,[3] Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique, Lecture Notes in Mathematics, 68 (1968). | MR | Zbl
, ,[4] Potential theory on harmonic spaces, Berlin-Heidelberg-New York, 1972. | MR | Zbl
, ,[5] On isolated singularities of solutions of second order elliptic differential equations, J. d'Anal. Math., 4 (1954-1956), 309-340. | MR | Zbl
, ,[6] Recherches axiomatiques sur la théorie des fonctions surhamoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. | Numdam | MR | Zbl
,[7] On the quotients of Green functions (preliminary version), Bielefeld, September 1980 (unpublished).
, ,[8] On the Harnack inequality for linear elliptic equations, J. d'Anal. Math., 4 (1956), 292-308. | MR | Zbl
,[9] On the Martin compactification of a bounded Lipschitz domain in a Riemannian manifold, Ann. Inst. Fourier, 28, 2 (1977), 25-52. | Numdam | MR | Zbl
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