Hölder Regularity for Solutions of Ultraparabolic Equations in Divergence Form

Abstract

We consider the second order differential equation $\sum\limits_{i,j = 1}^{m_0 } {\partial _{x_i } (a_{i,j} (x,t)\partial _{x_j } u) + \sum\limits_{i,j = 1}^N {b_{i,j} x_i \partial _{x_j } u - \partial _t u = \sum\limits_{j = 1}^{m_0 } {\partial _{x_j } F_j (x,t)} } }$, where (x,t)∈ℝ^N+1, 0<m ₀⩽N, the coefficients a _i,j belong to a suitable space of vanishing mean oscillation functions VMO _L and B=(b _i,j ) is a constant real matrix. The aim of this paper is to study interior regularity for weak solutions to the above equation assuming that F _j belong to a function space of Morrey type.