Geodesic
Global Hypoellipticity of a Class of Second Order Operators
Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 301-305

Voir la notice de l'article provenant de la source Cambridge University Press

We show that almost all perturbations P — λ, λ € C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values λ € C for which the operator is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.
DOI : 10.4153/CMB-1994-045-4
Mots-clés : 35H05, 35B10, 35B65, global hypoellipticity, periodic solutions 
Bergamasco, Adalberto P.; Zani, Sérgio Luís. Global Hypoellipticity of a Class of Second Order Operators. Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 301-305. doi: 10.4153/CMB-1994-045-4
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[1] 1. Greenfield, S.J., and Wallach, N., Global hypoellipticity and Liouville numbers, Proc. Amer. Math. Soc 31(1972), 112–114. Google Scholar

[2] 2. Greenfield, S.J., Remarks on global hypoellipticity, Trans. Amer. Math. Soc 183(1973), 153–164. Google Scholar

[3] 3. Herz, C. S., Functions which are divergences, Amer. J. Math. 92(1970), 641–656. Google Scholar

[4] 4. Leveque, W. J., Fundamentals of number theory, Reading, Addison-Wesley, 1977. Google Scholar

[5] 5. Mordell, L. J., Diophantine equations, New York, Academic Press, 1969. Google Scholar

[6] 6. Salamon, D. and Zehnder, E., KAM theory in configuration space, Comment. Math. Helv. 64(1989), 84–132. Google Scholar

[7] 7. Schwartz, L., Méthodes mathématiques pour les sciences physiques, Paris, Hermann, 1965. Google Scholar

[8] 8. Treves, F., Hypoelliptic partial differential equations of principal type. Sufficient conditions and necessary conditions. Comm. Pure Appl. Math. 34(1971), 631–670. Google Scholar

[9] 9. Yoshino, M., A class of globally hypoelliptic operators on the torus, Math. Z. 201(1989), 1–11. Google Scholar

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