In the theory of PDE, an a priori estimate (also called an apriori estimate or a priori bound) is an estimate derived before the solution is known to exist. One reason for their importance is that if one can prove an a priori estimate for solutions of a differential equation, then it is often possible to prove that solutions exist using the continuity method or a fixed point theorem. Here (download) is the brief summary for apriori estimate of linear Elliptic and Parabolic PDE in Chinese version.
