Removable singularities and Harnack inequality for nonlinear Hörmander degenerate subelliptic equations

Abstract

This paper concerns the quasilinear subelliptic function derived from Hörmander vector fields. Based on the significant work of J. Serrin in \cite{SER}, M. Meier in \cite{MM1}, and L. Capogna, D. Danielli and N. Garofalo in \cite{LC1,LDN}, we obtain the removable singularities and Harnack inequality by a sharp Sobolev inequalities under weaker integrability of coefficients in structure conditions. Furthermore, we get the Hölder continuity when domain $\hat{I}\text{c◯}$ is equiregular.