|
In the theory of partial differential equations, an ''a priori'' estimate (also called an apriori estimate or ''a priori'' bound) is an estimate for the size of a solution or its derivatives of a partial differential equation. ''A priori'' is Latin for "from before" and refers to the fact that the estimate for the solution is 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. ''A priori'' estimates were introduced and named by , who used them to prove existence of solutions to second order nonlinear elliptic equations in the plane. Some other early influential examples of ''a priori'' estimates include the Schauder estimates given by , and the estimates given by De Giorgi and Nash for second order elliptic or parabolic equations in many variables in their solution to Hilbert's nineteenth problem. ==References== * * * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「a priori estimate」の詳細全文を読む スポンサード リンク
|