  Two Theorems attributed to Hilbert-Weierstrass and Tonelli-Morrey
respectively are two classical studies for the regularity discussion around the
solutions of some problems in the realm of Calculus of Variations. Now, since
differential equations and optimal control problems with high-order have been
growing in the literature, addressing the regularity issues for these problems
should be paid more attention. In this regard, here, a generalization for the
regularity theorems will be presented. It is desired that these theorems will
be useful for researchers to prove the regularity properties of differential
equations or optimal control problems.
