The List of Hilbert’s Twenty-Three Problems: Hilbert’s Problem #19

Are The Solutions of Regular Problems in The Calculus of Variations Always Necessarily Analytic: Are the solutions of regular problems in the calculus of variations always necessarily analytic

Do solutions in general exist? The calculus of variations is a field concerned with optimizing certain types of functions called functionals. In his 19th and 20th problems, Hilbert asked whether certain classes of problems in the calculus of variations have solutions (his 20th) and, if so, whether those solutions are particularly smooth (19th).