Global analytic regularity for non-linear second order operators on the torus
HTML articles powered by AMS MathViewer
- by Chiara Boiti and Luisa Zanghirati
- Proc. Amer. Math. Soc. 131 (2003), 3783-3793
- DOI: https://doi.org/10.1090/S0002-9939-03-06940-5
- Published electronically: February 28, 2003
- PDF | Request permission
Abstract:
Assuming a subelliptic a-priori estimate we prove global analytic regularity for non-linear second order operators on a product of tori, using the method of majorant series.References
- S. Alinhac and G. Métivier, Propagation de l’analyticité des solutions de systèmes hyperboliques non-linéaires, Invent. Math. 75 (1984), no. 2, 189–204 (French). MR 732545, DOI 10.1007/BF01388563
- Jean-Michel Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 2, 209–246 (French). MR 631751, DOI 10.24033/asens.1404
- T. Gramchev, P. Popivanov, and M. Yoshino, Global properties in spaces of generalized functions on the torus for second order differential operators with variable coefficients, Rend. Sem. Mat. Univ. Politec. Torino 51 (1993), no. 2, 145–172 (1994). MR 1289385
- Pengfei Guan, Regularity of a class of quasilinear degenerate elliptic equations, Adv. Math. 132 (1997), no. 1, 24–45. MR 1488238, DOI 10.1006/aima.1997.1677
- Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
- David S. Tartakoff, Global (and local) analyticity for second order operators constructed from rigid vector fields on products of tori, Trans. Amer. Math. Soc. 348 (1996), no. 7, 2577–2583. MR 1344213, DOI 10.1090/S0002-9947-96-01573-5
- D.S. Tartakoff - L. Zanghirati, Analyticity of Solutions for Sums of Squares of Non-linear Vector Fields, to appear in Proc. A.M.S.
- Chao Jiang Xu, Régularité des solutions pour les équations aux dérivées partielles quasi linéaires non elliptiques du second ordre, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 9, 267–270 (French, with English summary). MR 785066
Bibliographic Information
- Chiara Boiti
- Affiliation: Dipartimento di Matematica, Via Machiavelli n.35, 44100 Ferrara, Italy
- Email: boiti@dm.unife.it
- Luisa Zanghirati
- Affiliation: Dipartimento di Matematica, Via Machiavelli n.35, 44100 Ferrara, Italy
- Email: zan@dns.unife.it
- Received by editor(s): July 4, 2002
- Published electronically: February 28, 2003
- Communicated by: David S. Tartakoff
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3783-3793
- MSC (2000): Primary 35B65, 35B45; Secondary 35H10, 35H20
- DOI: https://doi.org/10.1090/S0002-9939-03-06940-5
- MathSciNet review: 1998186