Geodesic
Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients
Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 441-456.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Precedenti risultati riguardanti il principio di massimo generalizzato e la valutazione del primo autovalore per operatori uniformemente ellittici di tipo variazionale vengono estesi agli operatori subellittici di tipo Heisenberg non simmetrici e a coefficienti discontinui. 
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Chicco, M.; Lancia, M. R. Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients. Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 441-456. http://geodesic.mathdoc.fr/item/BUMI_2001_8_4B_2_a8/

[1] A. Beurling-J. Deny, Dirichlet Spaces, Proc. Nat. Acad. Sc. USA, 45 (1959), 208-215. | MR | Zbl

[2] M. Biroli-U. Mosco, A Saint Venant principle for Dirichlet forms on discontinuous media, Ann. Mat. Pura Appl., 168 (1995), 125-181. | MR | Zbl

[3] M. Biroli-N. Tchou, Asymptotic Behaviour of Related Dirichlet problems Involving a Dirichlet Poincaré form, Zeith. Anal. Angew., 16 (1997), 281-309. | MR | Zbl

[4] J. M. Bony, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier Grenoble, 19 (1969), 277-304. | fulltext mini-dml | MR | Zbl

[5] L. Capogna-D. Danielli-N. Garofalo, Capacitary estimates and the local behaviour of solutions of nonlinear subelliptic equations, Amer. J. Math., 118 (1996), 1153-1196. | MR | Zbl

[6] M. Chicco, Principio di massimo generalizzato e valutazione del primo autovalore per problemi ellittici del secondo ordine di tipo variazionale, Ann. Mat. Pura Appl. (IV), 87 (1970), 1-10. | MR | Zbl

[7] M. Chicco, Principio di massimo forte per sottosoluzioni di equazioni ellittiche di tipo variazionale, Boll. Un. Mat. Ital. (3), 22 (1967), 368-372. | fulltext bdim | fulltext mini-dml | MR | Zbl

[8] R. R. Coifman-G. Weiss, Analyse harmonique non commutative sur certains éspaces homogénes, Lect. Notes in Math., 242, Springer-Verlag, Berlin-Heidelberg-New York (1971). | MR | Zbl

[9] B. Franchi-R. Serapioni-F. Serra Cassano, Rectifiability and perimeter in the Heisenberg group, preprint n. 371/p, Dip. Mat. Politecnico Milano (1999). | MR | Zbl

[10] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie group, Arkiv. fur Math., 136 (1973), 161-207. | MR | Zbl

[11] U. Gianazza, Regularity for degenerate obstacle problem, preprint n. 997, I.A.N., Pavia.

[12] D. Jerison, The Poincare inequality for vector fields satisfying Hormander's condition, Duke Math. J., 53 (1986), 503-523. | fulltext mini-dml | MR | Zbl

[13] D. S. Jerison-J. M. Lee, Extremal for the Sobolev inequality on the Heisenberg group and CR Yamabe Problem, Jour. Am. Math. Soc., 1 (1988), 1-13. | MR | Zbl

[14] M. G. Kreĭn-M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, A.M.S. Translations (1), 10 (1962), 199-325. | Zbl

[15] O. A. Ladyzhenskaya-N. N. Ural'Tseva, Linear and quasilinear elliptic equations, Academic Press, New York (1968). | Zbl

[16] M. R. Lancia, A note on $p$-capacity and Hausdorff measure for Heisenberg vector fields, in preparation.

[17] M. R. Lancia-M. V. Marchi, Liouville theorems for fuchsian-type operators on the Heisenberg Group, Zeit. An. und Anw., 16 (1997), 653-668. | MR | Zbl

[18] M. R. Lancia-M. V. Marchi, Harnack inequalities for non-symmetric operators of Hormander type with discontinuous coefficients, Adv. in Math. Sc. and Appl., 7 (1997), 833-857. | MR | Zbl

[19] A. Nagel-E. M. Stein-S. Wainger, Balls and metrics defined by vector fields I: Basic Properties, Acta Math., 155 (1985), 103-147. | MR | Zbl

[20] O. A. Oleinik-E. V. Radkewitch, Equazioni del secondo ordine con forma caratteristica non negativa, Veschi, Roma (1965).

[21] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Grenoble, 15 I (1965), 189-258. | fulltext mini-dml | MR | Zbl

[22] E. M. Stein, Harmonic Analysis, Princeton Math Series vol. 43, Princeton University Press (1993). | Zbl