Compact–analytical properties of variational functional in Sobolev spaces \(W^{1,p}\)

Abstract

In the work, conditions of well-definiteness, 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.