Multidimensional Variational Functionals with Subsmooth Integrands

Abstract

In the present paper, we establish a base of investigation of multidimensional variational functionals having \( C^1 \)-subsmooth or \( C^2 \)-subsmooth integrands. First, an estimate of the first \( K \)-variation for the multidimensional variational functional having a \( C^1 \)-subsmooth integrand is obtained and numerous partial cases are studied. Secondly, we have obtained \( C^1 \)-subsmooth generalizations of the basic variational lemma and Euler–Ostrogradskii equation. Finally, for the \( C^2 \)-subsmooth case, an estimate of the second \( K \)-variation is obtained and a series of the partial cases is studied as well.