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 Serie 8 4-B (2001), fasc. n.2, p. 441-456, Unione Matematica Italiana (English)
pdf (462 Kb), djvu (204 Kb). | MR1831998 | Zbl 1164.35328
Sunto
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.
Referenze Bibliografiche
[1]
A. BEURLING-
J. DENY,
Dirichlet Spaces,
Proc. Nat. Acad. Sc. USA,
45 (
1959), 208-215. |
MR 106365 |
Zbl 0089.08201[2]
M. BIROLI-
U. MOSCO,
A Saint Venant principle for Dirichlet forms on discontinuous media,
Ann. Mat. Pura Appl.,
168 (
1995), 125-181. |
MR 1378473 |
Zbl 0851.31008[3]
M. BIROLI-
N. TCHOU,
Asymptotic Behaviour of Related Dirichlet problems Involving a Dirichlet Poincaré form,
Zeith. Anal. Angew.,
16 (
1997), 281-309. |
MR 1459960 |
Zbl 0885.35011[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 262881 |
Zbl 0176.09703[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 1420920 |
Zbl 0878.35020[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 280858 |
Zbl 0207.10603[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 499948 |
Zbl 0224.43006[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 1871966 |
Zbl 1057.49032[10]
G. B. FOLLAND,
Subelliptic estimates and function spaces on nilpotent Lie group,
Arkiv. fur Math.,
136 (
1973), 161-207. |
MR 494315 |
Zbl 0312.35026[11] U. GIANAZZA, Regularity for degenerate obstacle problem, preprint n. 997, I.A.N., Pavia.
[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 924699 |
Zbl 0634.32016[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 0030.12902[15]
O. A. LADYZHENSKAYA-
N. N. URAL'TSEVA,
Linear and quasilinear elliptic equations,
Academic Press, New York (
1968). |
Zbl 0164.13002[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 1472723 |
Zbl 0884.35045[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 1476279 |
Zbl 0890.35003[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 793239 |
Zbl 0578.32044[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 192177 |
Zbl 0151.15401[22]
E. M. STEIN,
Harmonic Analysis,
Princeton Math Series vol.
43,
Princeton University Press (
1993). |
Zbl 0821.42001
Con il contributo del Ministero per i Beni e le Attività Culturali