The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
The authors consider a class of ultraparabolic equations with measurable coefficients of the form \[ \partial_t \, u= \sum_{i,j=1}^{m_0}X_i(a_{ij}(x,t)X_j\, u )+X_0 u. \] By choosing a new cut-off function, they prove the \(C^{\alpha}\) continuity of weak solutions extending analogous results proved by Lanconelli, Kogoj, Pascucci, Bonfiglioli, Uguzzoni and Polidoro. Their technique is based on a Poincare type inequality and a Harnack type estimate.
scientific article; zbMATH DE number 5866086