Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators

Abstract

In this paper it is studied the Hoelder-continuity of solutions of a linear degenerate elliptic equation of the form (∗) -Sum_ {i, j =1}^n (a_{i j} u_{x_i} )_{x_j} + V u = 0.It is proved that the solutions of (∗) are Hoelder-continuous if the coefficient V belongs to an appropriate "degenerate" Morrey space. Under some additional assumptions on the weight giving the degeneracy, the previous condition is also necessary.