Geodesic
Gradient estimates for elliptic systems in Carnot-Carathéodory spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 605-618.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $X=(X_1,X_2,\dots ,X_q)$ be a system of vector fields satisfying the Hör\-man\-der condition. We prove $L^{2,\lambda}_X$ local regularity for the gradient $Xu$ of a solution of the following strongly elliptic system $$ -X^{*}_{\alpha }(a^{\alpha \beta }_{ij}(x)X_{\beta } u^{j})= g_{i}-X^{*}_{\alpha } f^{\alpha }_{i}(x) \quad \forall i=1,2,\dots ,N, $$ where $a^{\alpha \beta }_{ij}(x)$ are bounded functions and belong to Vanishing Mean Oscillation space.
Classification : 35B65, 35D10, 35H20, 35J45, 35J50
Keywords: elliptic systems; Morrey space regularity; Carnot-Carathéodory metric 
@article{CMUC_2002__43_4_a2,
     author = {Di Fazio, Giuseppe and Fanciullo, Maria Stella},
     title = {Gradient estimates for elliptic systems in {Carnot-Carath\'eodory} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {605--618},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2002},
     mrnumber = {2045784},
     zbl = {1090.35058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a2/}
}
TY  - JOUR
AU  - Di Fazio, Giuseppe
AU  - Fanciullo, Maria Stella
TI  - Gradient estimates for elliptic systems in Carnot-Carathéodory spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2002
SP  - 605
EP  - 618
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a2/
LA  - en
ID  - CMUC_2002__43_4_a2
ER  - 
%0 Journal Article
%A Di Fazio, Giuseppe
%A Fanciullo, Maria Stella
%T Gradient estimates for elliptic systems in Carnot-Carathéodory spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2002
%P 605-618
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a2/
%G en
%F CMUC_2002__43_4_a2
Di Fazio, Giuseppe; Fanciullo, Maria Stella. Gradient estimates for elliptic systems in Carnot-Carathéodory spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 4, pp. 605-618. http://geodesic.mathdoc.fr/item/CMUC_2002__43_4_a2/