Hölder continuity for a class of X-elliptic equations with singular lower order term

Abstract

The regularity for a class of X-elliptic equations with lower order term $$ Lu + vu = - \sum\limits_{i,j = 1}^m {X_j *} (a_{ij} (x)X_i u) + vu = \mu $$ is studied, where X = {X1, ..., Xm} is a family of locally Lipschitz continuous vector fields, v is in certain Morrey type space and µ a nonnegative Radon measure. The Holder continuity of the solution is proved when µ satisfies suitable growth condition, and a converse result on the estimate of µ is obtained when u is in certain Holder class.