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Giuseppe Di Fazio, Maria Stella Fanciullo /H=@EAJ AIJE=JAI BH AEFJE? IOIJAI E +=HJ+=H=JD A@HO IF=?AI

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Giuseppe Di Fazio, Maria Stella Fanciullo

Gradient estimates for elliptic systems in Carnot-Caratheodory spaces

Comment.Math.Univ.Carolinae 43,4 (2002) 605-618.

Abstract: Let X = (X1, X2, ..., Xq) be a system of vector fields satisfying the H¨ormander condition. We prove L2,λX local regularity for the gradient Xu of a solution of the following strongly elliptic system

−Xα∗(aαβij (x)Xβuj) =gi−Xα∗fiα(x) ∀i= 1,2, ..., N,

where aαβij (x) are bounded functions and belong to Vanishing Mean Oscillation space.

Keywords: elliptic systems, Morrey space regularity, Carnot-Carath´eodory metric AMS Subject Classification: 35J50

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