Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients

M. Chicco; M. R. Lancia

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 2, page 441-456
  • ISSN: 0392-4041

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Chicco, M., and Lancia, M. R.. "Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients." Bollettino dell'Unione Matematica Italiana 4-B.2 (2001): 441-456. <http://eudml.org/doc/195843>.

@article{Chicco2001,
author = {Chicco, M., Lancia, M. R.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {441-456},
publisher = {Unione Matematica Italiana},
title = {Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients},
url = {http://eudml.org/doc/195843},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Chicco, M.
AU - Lancia, M. R.
TI - Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/6//
PB - Unione Matematica Italiana
VL - 4-B
IS - 2
SP - 441
EP - 456
LA - eng
UR - http://eudml.org/doc/195843
ER -

References

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  1. BEURLING, A.- DENY, J., Dirichlet Spaces, Proc. Nat. Acad. Sc. USA, 45 (1959), 208-215. Zbl0089.08201MR106365
  2. BIROLI, M.- MOSCO, U., A Saint Venant principle for Dirichlet forms on discontinuous media, Ann. Mat. Pura Appl., 168 (1995), 125-181. Zbl0851.31008MR1378473
  3. BIROLI, M.- TCHOU, N., Asymptotic Behaviour of Related Dirichlet problems Involving a Dirichlet Poincaré form, Zeith. Anal. Angew., 16 (1997), 281-309. Zbl0885.35011MR1459960
  4. BONY, J. M., 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. Zbl0176.09703MR262881
  5. CAPOGNA, L.- DANIELLI, D.- GAROFALO, N., Capacitary estimates and the local behaviour of solutions of nonlinear subelliptic equations, Amer. J. Math., 118 (1996), 1153-1196. Zbl0878.35020MR1420920
  6. CHICCO, M., 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. Zbl0207.10603MR280858
  7. CHICCO, M., Principio di massimo forte per sottosoluzioni di equazioni ellittiche di tipo variazionale, Boll. Un. Mat. Ital. (3), 22 (1967), 368-372. Zbl0149.32002MR224999
  8. COIFMAN, R. R.- WEISS, G., Analyse harmonique non commutative sur certains éspaces homogénes, Lect. Notes in Math., 242, Springer-Verlag, Berlin-Heidelberg-New York (1971). Zbl0224.43006MR499948
  9. FRANCHI, B.- SERAPIONI, R.- SERRA CASSANO, F., Rectifiability and perimeter in the Heisenberg group, preprint n. 371/p, Dip. Mat. Politecnico Milano (1999). Zbl1057.49032MR1871966
  10. FOLLAND, G. B., Subelliptic estimates and function spaces on nilpotent Lie group, Arkiv. fur Math., 136 (1973), 161-207. Zbl0312.35026MR494315
  11. GIANAZZA, U., Regularity for degenerate obstacle problem, preprint n. 997, I.A.N., Pavia. 
  12. JERISON, D., The Poincare inequality for vector fields satisfying Hormander's condition, Duke Math. J., 53 (1986), 503-523. Zbl0614.35066MR850547
  13. JERISON, D. S.- LEE, J. M., Extremal for the Sobolev inequality on the Heisenberg group and CR Yamabe Problem, Jour. Am. Math. Soc., 1 (1988), 1-13. Zbl0634.32016MR924699
  14. KREĬN, M. G.- RUTMAN, M. A., Linear operators leaving invariant a cone in a Banach space, A.M.S. Translations (1), 10 (1962), 199-325. Zbl0030.12902
  15. LADYZHENSKAYA, O. A.- URAL'TSEVA, N. N., Linear and quasilinear elliptic equations, Academic Press, New York (1968). Zbl0164.13002
  16. LANCIA, M. R., A note on p -capacity and Hausdorff measure for Heisenberg vector fields, in preparation. 
  17. LANCIA, M. R.- MARCHI, M. V., Liouville theorems for fuchsian-type operators on the Heisenberg Group, Zeit. An. und Anw., 16 (1997), 653-668. Zbl0884.35045MR1472723
  18. LANCIA, M. R.- MARCHI, M. V., Harnack inequalities for non-symmetric operators of Hormander type with discontinuous coefficients, Adv. in Math. Sc. and Appl., 7 (1997), 833-857. Zbl0890.35003MR1476279
  19. NAGEL, A.- STEIN, E. M.- WAINGER, S., Balls and metrics defined by vector fields I: Basic Properties, Acta Math., 155 (1985), 103-147. Zbl0578.32044MR793239
  20. OLEINIK, O. A.- RADKEWITCH, E. V., Equazioni del secondo ordine con forma caratteristica non negativa, Veschi, Roma (1965). 
  21. STAMPACCHIA, G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Grenoble, 15 I (1965), 189-258. Zbl0151.15401MR192177
  22. STEIN, E. M., Harmonic Analysis, Princeton Math Series vol. 43, Princeton University Press (1993). Zbl0821.42001

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