An integral inequality for differentiable functions of several variables (Q1059164)

The integral inequality established in this paper is a consequence of the isoperimetric inequality and generalizes some earlier results of the author [Sib. Mat. Zh. 7, No.5, 1106-1114 (1966; Zbl 0158.327)]. As an application it is shown that some transformations \(f: U\to R^ n\) (U open in \(R^ n\), f in \(W^ 1_{k,loc}(U))\) satisfy the Hölder condition on every compact subset \(A\subset U.\)