Abstract
This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.
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References
[BT] M. S. Baouendi and F. Treves,A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math.,113 (1981), 387–421.
[BH1] S. Berhanu and J. Hounie,An F. and M. Riesz theorem for planar vector fields, Math. Ann.,320, (2001), 463–485.
[BH2] S. Berhanu and J. HounieOn boundary properties of solutions of complex vector fields, to appear in Jour of Functional Analysis.
[C] P. Cohen,The non-uniqueness of the Cauchy problem, O.N.R. Tech. Report,93 (1960), Stanford.
[Co] P. Cordaro,Approximate solutions in locally integrable structures, Fields Institute Communications volume: Differential Equations and Dynamical Systems (in honor to Waldyr Muniz Oliva), to appear
[Du] P. Duren,Theory of H p spaces, Academic Press, 1970.
[F] P. Fatou,Séries trigonométriques e séries de Taylor, Acta Math.,30 (1906), 335–400.
[HM] J. Hounie and J. MalaguttiOn the convergence of the Baouendi-Treves approximation formula, Comm. P.D.E.,23 (1998), 1305–1347.
[HT] J. Hounie and J. Tavares,On removable singularities of locally solvable differential operators, Invent. Math.,126 (1996), 589–623.
[Hor] L. Hörmander,The Analysis of linear partial differential operators I, Springer-Verlag, 1990.
[J] B. Jöricke,Deformation of CR manifolds, minimal points and CR manifolds with the microlocal analytic extension property, J. Geom. Anal., (1996), 555–611.
[RR] F. Riesz and M. Riesz,Über die Randwerte einer analytischen Funktion Quatrième Congrès de Math. Scand. Stockholm, (1916), 27–44.
[T1] F. Treves,Hypo-analytic structures, local theory, Princeton University Press, 1992.
[T2] F. Treves,Approximation and representation of solutions in locally integrable structures with boundary, Aspects of Math. and Applications, (1986), 781–816.
[T3] F. Treves,Approximation and representation of functions and distributions annihilated by a system of complex vector fields, Centre de Mathématiques. École Polytechnique, Palaiseau, France, 1981.
[Z] C. ZuilyUniqueness and non-uniqueness in the Cauchy Problem, Birkhäuser, Boston-Basel-Stuttgart, 1983.
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Dedicated to Constantine Dafermos on his 60th birthday
Work supported in part by CNPq, FINEP, FAPESP and a Research Incentive Fund grant of Temple University.
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Berhanu, S., Hounie, J. A strong uniqueness theorem for planar vector fields. Bol. Soc. Bras. Mat 32, 359–376 (2001). https://doi.org/10.1007/BF01233672
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DOI: https://doi.org/10.1007/BF01233672