Di Fazio, Giuseppe and Zamboni, Pietro:
Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.2, p. 485-504, (English)
pdf (447 Kb), djvu (170 Kb). | MR 2233147 | Zbl 1178.35163
Sunto
In questa nota proviamo la disuguaglianza di Harnack per le soluzioni deboli di una equazione sub-ellittica quasilineare del tipo \begin{equation*}\tag{*}\sum_{J=1}^{m} X_{j}^{*}A_{j}(x, u(x), Xu(x)) + B(x, u(x), Xu(x)) = 0,\end{equation*} dove $X_{1}, \ldots, X_{m}$ denotano un sistema non commutativo di campi vettoriali localmente lipschitziani. Come conseguenza otteniamo la continuità delle soluzioni deboli della (*).
Referenze Bibliografiche
[2]
L. CAPOGNA -
D. DANIELLI -
N. GAROFALO,
An embedding theorem and the Harnack inequality for nonlinear subelliptic equations,
Comm. P.D.E.,
18 (
1993), 1765-1794. |
fulltext (doi) |
MR 1239930 |
Zbl 0802.35024[4]
F. CHIARENZA -
E. FABES -
N. GAROFALO,
Harnack's inequality for Schrödinger operators and continuity of solutions,
Proc. A.M.S.,
98 (
1986), 415-425. |
fulltext (doi) |
MR 857933 |
Zbl 0626.35022[5]
D. DANIELLI,
A Fefferman-Phong type inequality and applications to quasilinear subelliptic equations,
Potential Analysis,
115 (
1999), 387-413. |
fulltext (doi) |
MR 1719837 |
Zbl 0940.35057[6]
D. DANIELLI -
N. GAROFALO -
D. NHIEU,
Trace inequalities for Carnot-Caratheodory spaces and applications,
Ann. Scuola Norm. Sup. Pisa,
4 (
1998), 195-252. |
fulltext EuDML |
MR 1664688 |
Zbl 0938.46036[8]
G. DI FAZIO -
P. ZAMBONI Hölder continuity for quasilinear subelliptic equations in Carnot Caratheodory spaces,
Math. Nachr. 272 (
2004), 3-10. |
fulltext (doi) |
MR 2079757 |
Zbl 1149.35347[9] O.A. LADYZHENSKAYA - N. URALCEVA, Linear and quasilinear elliptic equations, Academic Press (1968).
[10]
G. LIEBERMAN,
Sharp forms of Estimates for Subsolutions and Supersolutions of Quasilinear Elliptic Equations Involving Measures,
Comm. P.D.E.,
18 (
1993), 1191-1212. |
fulltext (doi) |
MR 1233190 |
Zbl 0802.35041[11]
M.A. RAGUSA -
P. ZAMBONI,
Local regularity of solutions to quasilinear elliptic equations with general structure,
Communications in Applied Analysis,
3 (
1999), 131-147. |
MR 1669745 |
Zbl 0922.35050[13]
J.M. RAKOTOSON -
W.P. ZIEMER,
Local behavior of solutions of quasilinear elliptic equations with general structure,
Trans. A. M. S.,
319 (
1990), 747-764. |
fulltext (doi) |
MR 998128 |
Zbl 0708.35023[15]
J. SERRIN -
H. ZOU,
Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities,
Acta Math.,
189, n. 1 (
2002), 79-142. |
fulltext (doi) |
MR 1946918 |
Zbl 1059.35040[16]
P. ZAMBONI,
Harnack's inequality for quasilinear elliptic equations with coefficients in Morrey spaces,
Rend. Sem. Mat. Univ. Padova,
89 (
1993), 87-96. |
fulltext EuDML |
MR 1229045 |
Zbl 0802.35043[17]
P. ZAMBONI,
Local boundedness of solutions of quasilinear elliptic equations with coefficients in Morrey spaces,
Boll. Un. Mat. It.,
8-B (
1994), 985-997. |
MR 1315830 |
Zbl 0827.35040[18]
P. ZAMBONI,
Local behavior of solutions of quasilinear elliptic equations with coefficients in Morrey Spaces,
Rendiconti di Matematica, Serie VII,
15 (
1995), 251-262. |
MR 1339243 |
Zbl 0832.35046[19]
P. ZAMBONI,
Unique continuation for non-negative solutions of quasilinear elliptic equations,
Bull. Austral. Math. Soc.,
64 (
2001), 149-156. |
fulltext (doi) |
MR 1848087 |
Zbl 0989.47037
Con il contributo del Ministero per i Beni e le Attività Culturali