Invarianzeigenschaften bei Variationsproblemen mit nichtdifferenzierbaren Integranden. (Invariance properties for variational problems with nonsmooth integrands) (Q1097509)

Summary: A new proof of Rvachev's invariance theorem [see \textit{M. A. Rvachev}, Kibernetika, Kiev 1974, No.6, 116-120 (1974; Zbl 0306.49015); Dokl. Akad. Nauk SSSR 219, 46-48 (1974; Zbl 0329.49031); and Funkts. Anal. Prilozh. 11, No.2, 58-66 (1977; Zbl 0349.49022)] for variational problems with nonsmooth but convex Lagrangians is given. This proof is valid even for the multidimensional case. The results are extended to the physically interesting case where the invariance of the Lagrangian can only be obtained with the help of some divergence terms and to the case where the Lagrangian is merely convex for some part of the variables.