Multidimensional variational functionals with subsmooth integrands

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 $K$-variational is obtained and a series of the partial cases is studied as well.