Hölder regularity for weak solutions to divergence form degenerate quasilinear parabolic systems (Q2260427)

The author considers diagonal, divergence-form, degenerate, quasilinear parabolic systems related to Hörmander-type vector fields \[ u_t^i +X^\ast_\alpha(a^{\alpha\beta}_i (z,u)X_\beta u^i)= g_i(z,u,Xu)+X^\ast_\alpha f_i^\alpha(z). \] The Hölder regularity of the solutions is established by deriving a parabolic Poincaré inequality and the higher integrability of gradients of the weak solutions.