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.