(untitled) (Journal of Partial Differential Equations, 1997)
In this paper we derive a priori estimates in the Campanato space L^2,μ(Q_T) for solutions of tbe following parabolic equation u_t - ∂∂x_i(a_ij(x,t)u_x_j+a_iu) + b_iu_x_i + cu = ∂∂_x_if_i + f_0 where a_ij(x, t) are assumed to be measurable and satisfy the ellipticity condition. The proof is based on accurate DeGiorgi-Nash-Moser's estimate and a modified Poincare's inequality. These estimates are very useful in the study of the regularity of solutions for some nonlinear problems. As a concrete example, we obtain the classical solvability for a strongly coupled parabolic system arising from the thermistor problem.