  It is well-known that the embedding of the Sobolev space of weakly
differentiable functions into H\"{o}lder spaces holds if the integrability
exponent is higher than the space dimension of the domain. In this paper, the
embedding of the Sobolev functions into the H\"{o}lder spaces is expressed in
terms of the minimal weak differentiability requirement independent of the
integrability exponent. The proof is based on the generalized Newton-Leibniz
formula in the rectangular prism and inductive application of the Sobolev trace
embedding results. The particular motivation for the new embedding theorem
appears in proving compactness of the family of multilinear interpolations of
discrete grid functions arising as solutions of the discretized PDE problems.
