Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields

Abstract

In this paper we obtain the Holder continuity property of the solutions for a class of degenerate Schrodinger equation generated by the vector fields: $$- \sum\limits_{i,j = 1}^m {X_j^* \left( {a_{ij} \left( x \right)X_i u} \right) + \vec bXu + vu = 0,}$$ where X = {X1, ...,Xm} is a family of C∞ vector fields satisfying the Hormander condition, and the lower order terms belong to an appropriate Morrey type space.