Compact-analytical properties of variational functional in Sobolev spaces $W^{1,p}$

In the work, conditions of welldefiniteness, compact continuity, compact differentiability and multiple compact differentiability of the Euler–Lagrange one-dimensional variational functional in Sobolev–Bochner spaces $W^{1,p}([a;b],F)$ are obtained in terms of belonging of the integrand to the corresponding Weierstrass pseudopolynomial classes.