Duke Mathematical Journal

An extension of Hörmander’s theorem for infinitely degenerate second-order operators

Article information

Source
Duke Math. J. Volume 78, Number 3 (1995), 453-475.

Dates
First available in Project Euclid: 20 February 2004

http://projecteuclid.org/euclid.dmj/1077285944

Digital Object Identifier
doi:10.1215/S0012-7094-95-07822-3

Mathematical Reviews number (MathSciNet)
MR1334203

Zentralblatt MATH identifier
0840.60053

Subjects
Primary: 35H05

Citation

Bell, Denis R.; Mohammed, Salah-Eldin A. An extension of Hörmander’s theorem for infinitely degenerate second-order operators. Duke Math. J. 78 (1995), no. 3, 453--475. doi:10.1215/S0012-7094-95-07822-3. http://projecteuclid.org/euclid.dmj/1077285944.

References

• [B] D. R. Bell, The Malliavin calculus, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 34, Longman Scientific & Technical, Harlow, 1987.
• [BM] D. R. Bell and S.-E. A. Mohammed, Hypoelliptic parabolic operators with exponential degeneracies, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 11, 1059–1064.
• [FP] C. Fefferman and D. Phong, Subelliptic eigenvalue problems, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981), Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 590–606.
• [H] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171.
• [IW] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam, 1989.
• [KS] 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.
• [M1] P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976), Wiley, New York, 1978, pp. 195–263.
• [M2] P. Malliavin, $C\spk$-hypoellipticity with degeneracy. II, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978), Academic Press, New York, 1978, pp. 327–340.
• [Mo] Y. Morimoto, Hypoellipticity for infinitely degenerate elliptic operators, Osaka J. Math. 24 (1987), no. 1, 13–35.
• [N] J. Norris, Simplified Malliavin calculus, Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, Berlin, 1986, pp. 101–130.
• [OR] O. A. Oleĭ nik and E. V. Radkevič, Second order equations with nonnegative characteristic form, Plenum Press, New York, 1973.
• [S] D. Stroock, The Malliavin calculus, a functional analytic approach, J. Funct. Anal. 44 (1981), no. 2, 212–257.