Episode 1783
A priori estimate
Tue, 2022-Mar-22 00:07 UTC
Length - 1:58
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Welcome to random Wiki of the Day where we read the summary of a random Wikipedia page every day.
The random article for Tuesday, 22 March 2022 is A priori estimate.
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 Sergei Natanovich Bernstein (1906, 1910), 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 Schauder (1934, 1937), 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.
This recording reflects the Wikipedia text as of 00:07 UTC on Tuesday, 22 March 2022.
For the full current version of the article, see A priori estimate on Wikipedia.
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This has been Joanna Neural. Thank you for listening to random Wiki of the Day.
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