Loss of derivatives for systems of complex vector fields and sums of squares
HTML articles powered by AMS MathViewer
- by Tran Vu Khanh, Stefano Pinton and Giuseppe Zampieri
- Proc. Amer. Math. Soc. 140 (2012), 519-530
- DOI: https://doi.org/10.1090/S0002-9939-2011-11287-5
- Published electronically: September 27, 2011
- PDF | Request permission
Abstract:
We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.References
- Antonio Bove, Makhlouf Derridj, Joseph J. Kohn, and David S. Tartakoff, Sums of squares of complex vector fields and (analytic-) hypoellipticity, Math. Res. Lett. 13 (2006), no. 5-6, 683–701. MR 2280767, DOI 10.4310/MRL.2006.v13.n5.a1
- Denis R. Bell and Salah Eldin A. Mohammed, An extension of Hörmander’s theorem for infinitely degenerate second-order operators, Duke Math. J. 78 (1995), no. 3, 453–475. MR 1334203, DOI 10.1215/S0012-7094-95-07822-3
- Michael Christ, Hypoellipticity of the Kohn Laplacian for three-dimensional tubular Cauchy-Riemann structures, J. Inst. Math. Jussieu 1 (2002), no. 2, 279–291. MR 1954822, DOI 10.1017/S1474-748002000063
- V. S. Fediĭ, A certain criterion for hypoellipticity, Mat. Sb. (N.S.) 85 (127) (1971), 18–48 (Russian). MR 0287160
- G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
- Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
- J. J. Kohn, Hypoellipticity at points of infinite type, Analysis, geometry, number theory: the mathematics of Leon Ehrenpreis (Philadelphia, PA, 1998) Contemp. Math., vol. 251, Amer. Math. Soc., Providence, RI, 2000, pp. 393–398. MR 1771281, DOI 10.1090/conm/251/03882
- J. J. Kohn, Superlogarithmic estimates on pseudoconvex domains and CR manifolds, Ann. of Math. (2) 156 (2002), no. 1, 213–248. MR 1935846, DOI 10.2307/3597189
- J. J. Kohn, Hypoellipticity and loss of derivatives, Ann. of Math. (2) 162 (2005), no. 2, 943–986. With an appendix by Makhlouf Derridj and David S. Tartakoff. MR 2183286, DOI 10.4007/annals.2005.162.943
- J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 181815, DOI 10.1002/cpa.3160180305
- S. Kusuoka and D. Stroock, Applications of the Malliavin calculus. II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985), no. 1, 1–76. MR 783181
- Yoshinori Morimoto, Hypoellipticity for infinitely degenerate elliptic operators, Osaka J. Math. 24 (1987), no. 1, 13–35. MR 881744
- Cesare Parenti and Alberto Parmeggiani, On the hypoellipticity with a big loss of derivatives, Kyushu J. Math. 59 (2005), no. 1, 155–230. MR 2134059, DOI 10.2206/kyushujm.59.155
- E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math. 69 (1982), no. 2, 209–216. MR 674401, DOI 10.1007/BF01399501
- David S. Tartakoff, Analyticity for singular sums of squares of degenerate vector fields, Proc. Amer. Math. Soc. 134 (2006), no. 11, 3343–3352. MR 2231919, DOI 10.1090/S0002-9939-06-08419-X
Bibliographic Information
- Tran Vu Khanh
- Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
- MR Author ID: 815734
- Email: khanh@math.unipd.it
- Stefano Pinton
- Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
- Email: pinton@math.unipd.it
- Giuseppe Zampieri
- Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
- Email: zampieri@math.unipd.it
- Received by editor(s): September 30, 2010
- Published electronically: September 27, 2011
- Communicated by: Mei-Chi Shaw
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 519-530
- MSC (2010): Primary 32W05, 32W25, 32T25
- DOI: https://doi.org/10.1090/S0002-9939-2011-11287-5
- MathSciNet review: 2846320