Classification: 35F05, 30G20
Keywords: characteristic set, complex vector field, infinite type, solvability
@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}, publisher = {Association des Annales de l'institut Fourier}, volume = {55}, number = {1}, year = {2005}, pages = {77-112}, doi = {10.5802/aif.2090}, mrnumber = {2141289}, zbl = {1063.35051}, language = {en}, url = {https://aif.centre-mersenne.org/item/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. https://aif.centre-mersenne.org/item/AIF_2005__55_1_77_0/
[B1] Perturbation of globally hypoelliptic operators, J. Differential Equations, Tome 114 (1994), pp. 513-526 | Article | MR 1303037 | Zbl 0815.35009
[B2] Remarks about global analytic hypoellipticity, Trans. Amer. Math. Soc., Tome 351 (1999), pp. 4113-4126 | Article | MR 1603878 | Zbl 0932.35046
[BCH] Global properties of a class of vector fields in the plane, J. Diff. Equations, Tome 74 (1988), pp. 179-199 | Article | MR 952894 | Zbl 0662.58021
[BCM] Globally hypoelliptic systems of vector fields, J. Funct. Analysis, Tome 114 (1993), pp. 267-285 | Article | MR 1223704 | Zbl 0777.58041
[BCP] Global solvability for a class of complex vector fields on the two-torus, Comm. Partial Differential Equations, Tome 29 (2004), pp. 785-819 | Article | MR 2059148 | Zbl 1065.35088
[BgM] Semiglobal solvability of a class of planar vector fields of infinite type, Mat. Contemp., Tome 18 (2000), pp. 31-42 | MR 1812861 | Zbl 0983.35036
[BhM1] On rotationally invariant vector fields in the plane, Manuscripta Math., Tome 89 (1996), pp. 355-371 | Article | MR 1378599 | Zbl 0858.35021
[BhM2] Global properties of a class of planar vector fields of infinite type, Comm. Partial Differential Equations, Tome 22 (1997), pp. 99-142 | MR 1434140 | Zbl 0882.35029
[BHS] A generalized similarity principle for complex vector fields and applications, Trans. Amer. Math. Soc., Tome 353 (2001), pp. 1661-1675 | Article | MR 1806725 | Zbl 0982.35030
[BT] A property of functions and distributions annihilated by locally integrable system of vector fields, Ann. of Math., Tome 113 (1981), pp. 341-421 | MR 607899 | Zbl 0491.35036
[CG] Normalization of complex-valued planar vector fields which degenerate along a real curve, Adv. Math., Tome 184 (2004), pp. 89-118 | Article | MR 2047850 | Zbl 02081957
[CH] Global analytic hypoellipticity for a class of degenerate elliptic operators on the torus, Math. Res. Letters, Tome 1 (1994), pp. 501-510 | MR 1302393 | Zbl 0836.35036
[CT] Homology and cohomology in hypoanalytic structures of the hypersurface type, J. Geo. Analysis, Tome 1 (1991), pp. 39-70 | MR 1097935 | Zbl 0724.32009
[G] Hypoelliptic vector fields and continued fractions, Proc. Amer. Math. Soc., Tome 31 (1972), pp. 115-118 | Article | MR 301459 | Zbl 0229.35024
[GPY] Global properties in spaces of generalized functions on the torus for second-order differential operators with variable coefficients, Rend. Sem. Mat. Univ. Pol. Torino, Tome 51 (1993), pp. 145-172 | MR 1289385 | Zbl 0824.35027
[H] The analysis of linear partial differential operators IV, New York (1984) | MR 781537 | Zbl 0612.35001
[M1] On the similarity principle for planar vector fields: applications to second order pde, J. Differential Equations, Tome 157 (1999), pp. 1-19 | Article | MR 1710011 | Zbl 0937.35079
[M2] On real analytic planar vector fields near the characteristic set, Contemp. Math., Tome 251 (2000), pp. 429-438 | MR 1771284 | Zbl 0960.35016
[M3] On planar elliptic structures with infinite type degeneracy, J. Funct. Anal., Tome 179 (2001), pp. 333-373 | Article | MR 1809114 | Zbl 0973.35083
[M4] Elliptic planar vector fields with degeneracies (Trans. Amer. Math. Soc., to appear) | MR 2159708 | Zbl 02188287
[NT] Solvability of a first order linear partial differential equation, Comm. Pure Applied Math., Tome 16 (1963), pp. 331-351 | Article | MR 163045 | Zbl 0117.06104
[T1] Remarks about certain first-order linear PDE in two variables, Comm. Partial Differential Equations, Tome 5 (1980), pp. 381-425 | Article | MR 567779 | Zbl 0523.35012
[T2] Hypo-analytic structures: local theory, Princeton University Press (1992) | MR 1200459 | Zbl 0787.35003
[V] Generalized analytic functions (1962) | MR 150320 | Zbl 0100.07603