Geodesic
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 provenant de la source Biblioteca Digitale Italiana di Matematica

We prove Harnack inequality for weak solutions to quasilinear subelliptic equation of the following kind \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*} where $X_{1}, \ldots, X_{m}$ are a system of non commutative locally Lipschitz vector fields. As a consequence, the weak solutions of (*) are continuous. 
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     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},
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     year = {2006},
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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. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_2_a11/