Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces

Giuseppe Di Fazio; Pietro Zamboni

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 485-504
  • ISSN: 0392-4041

Abstract

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We prove Harnack inequality for weak solutions to quasilinear subelliptic equation of the following kind ∑ J = 1 m X j * ⁢ A j ⁢ ( x , u ⁢ ( x ) , X ⁢ u ⁢ ( x ) ) + B ⁢ ( x , u ⁢ ( x ) , X ⁢ u ⁢ ( x ) ) = 0 , where X 1 , … , X m are a system of non commutative locally Lipschitz vector fields. As a consequence, the weak solutions of (*) are continuous.

How to cite

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Di Fazio, Giuseppe, and Zamboni, Pietro. "Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 485-504. <http://eudml.org/doc/289621>.

@article{DiFazio2006,
abstract = {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.},
author = {Di Fazio, Giuseppe, Zamboni, Pietro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {485-504},
publisher = {Unione Matematica Italiana},
title = {Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces},
url = {http://eudml.org/doc/289621},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Di Fazio, Giuseppe
AU - Zamboni, Pietro
TI - Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 485
EP - 504
AB - 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.
LA - eng
UR - http://eudml.org/doc/289621
ER -

References

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