We study the solvability of equations associated with a complex vector field in with or coefficients. We assume that is elliptic everywhere except on a simple and closed curve . We assume that, on , is of infinite type and that vanishes to a constant order. The equations considered are of the form , with satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of is , the equation is solvable in the category but not in the category.
On étudie la résolubilité des équations associées à un champ de vecteurs complexe dans à coefficients de classe ou . On suppose que est partout elliptique, sauf le long d’une courbe simple et fermée . Sur , on suppose que est de type infini et que s’annule à un ordre constant. Les équations considerées sont de la forme , où satisfait des conditions de compatibilité. On prouve, en particulier, que lorsque l’ordre d’annulation de est , l’équation est résoluble dans la catégorie mais pas dans la catégorie .
Keywords: characteristic set, complex vector field, infinite type, solvability
Mot clés : ensemble caractéristique, champ de vecteur complexe, type infini, résolubilité
@article{AIF_2005__55_1_77_0, author = {P. Bergamasco, Alberto and Meziani, Abdelhamid}, title = {Solvability near the characteristic set for a class of planar vector fields of infinite type}, journal = {Annales de l'Institut Fourier}, pages = {77--112}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2090}, mrnumber = {2141289}, zbl = {1063.35051}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2090/} }
TY - JOUR AU - P. Bergamasco, Alberto AU - Meziani, Abdelhamid TI - Solvability near the characteristic set for a class of planar vector fields of infinite type JO - Annales de l'Institut Fourier PY - 2005 SP - 77 EP - 112 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2090/ DO - 10.5802/aif.2090 LA - en ID - AIF_2005__55_1_77_0 ER -
%0 Journal Article %A P. Bergamasco, Alberto %A Meziani, Abdelhamid %T Solvability near the characteristic set for a class of planar vector fields of infinite type %J Annales de l'Institut Fourier %D 2005 %P 77-112 %V 55 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2090/ %R 10.5802/aif.2090 %G en %F AIF_2005__55_1_77_0
P. Bergamasco, Alberto; Meziani, Abdelhamid. Solvability near the characteristic set for a class of planar vector fields of infinite type. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 77-112. doi : 10.5802/aif.2090. http://archive.numdam.org/articles/10.5802/aif.2090/
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