Geodesic
Multidimensional variational functionals with subsmooth integrands
Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 54-75

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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. 
@article{EMJ_2015_6_3_a4,
     author = {I. V. Orlov and A. V. Tsygankova},
     title = {Multidimensional variational functionals with subsmooth integrands},
     journal = {Eurasian mathematical journal},
     pages = {54--75},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a4/}
}
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I. V. Orlov; A. V. Tsygankova. Multidimensional variational functionals with subsmooth integrands. Eurasian mathematical journal, Tome 6 (2015) no. 3, pp. 54-75. http://geodesic.mathdoc.fr/item/EMJ_2015_6_3_a4/