Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 485-504.

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

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 (*).
@article{BUMI_2006_8_9B_2_a11,
     author = {Di Fazio, Giuseppe and Zamboni, Pietro},
     title = {Local regularity of solutions to quasilinear subelliptic equations in {Carnot} {Caratheodory} spaces},
     journal = {Bollettino della Unione matematica italiana},
     pages = {485--504},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {2},
     year = {2006},
     zbl = {1178.35163},
     mrnumber = {2233147},
     language = {it},
     url = {https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a11/}
}
TY  - JOUR
AU  - Di Fazio, Giuseppe
AU  - Zamboni, Pietro
TI  - Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces
JO  - Bollettino della Unione matematica italiana
PY  - 2006
SP  - 485
EP  - 504
VL  - 9B
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a11/
LA  - it
ID  - BUMI_2006_8_9B_2_a11
ER  - 
%0 Journal Article
%A Di Fazio, Giuseppe
%A Zamboni, Pietro
%T Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces
%J Bollettino della Unione matematica italiana
%D 2006
%P 485-504
%V 9B
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a11/
%G it
%F BUMI_2006_8_9B_2_a11
Di Fazio, Giuseppe; Zamboni, Pietro. Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 485-504. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a11/

[1] S. Buckley, Inequalities of John Nirenberg type in doubling spaces, J. Anal. Math., 79 (1999), 215-240. | fulltext (doi) | MR | Zbl

[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 | Zbl

[3] F. Chiarenza, Regularity for solutions of quasilinear elliptic equations under minimal assumptions, Potential Analysis, 4 (1995), 325-334. | fulltext (doi) | MR | Zbl

[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 | Zbl

[5] D. Danielli, A Fefferman-Phong type inequality and applications to quasilinear subelliptic equations, Potential Analysis, 115 (1999), 387-413. | fulltext (doi) | MR | Zbl

[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 | Zbl

[7] G. Di Fazio - P. Zamboni, A Fefferman-Poincaré type inequality for Carnot-Carathéodory vector fields, Proc. A.M.S., 130 (2002), 2655-2660. | fulltext (doi) | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[12] J.M. Rakotoson, Quasilinear equations and Spaces of Campanato-Morrey type, Comm. P.D.E., 16 (1991), 1155-1182. | fulltext (doi) | MR | Zbl

[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 | Zbl

[14] J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math., 111 (1964), 247-302. | fulltext (doi) | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[19] P. Zamboni, Unique continuation for non-negative solutions of quasilinear elliptic equations, Bull. Austral. Math. Soc., 64 (2001), 149-156. | fulltext (doi) | MR | Zbl

[20] P. Zamboni The Harnack inequality for quasilinear elliptic equations under minimal assumptions, Manuscripta Math., 102 (2000), 311-323. | fulltext (doi) | MR | Zbl