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Partial interior regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups: the sub-quadratic controllable case
We consider nonlinear sub-elliptic systems with Dini continuous coefficients for the case $1< m<2$ in Carnot groups and prove a $C^{1}$ -partial regularity result for weak solutions under the controllable growth conditions. Our method of proof for sub-elliptic systems is based on a generalization of the technique of $\mathcal {A}$ …