A new proof of Rvacev’s invariance theorem 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.
Cite this article
Wolfgang Thämelt, Invarianzeigenschaften bei Variationsproblemen mit nichtdifferenzierbaren Integranden. Z. Anal. Anwend. 5 (1986), no. 6, pp. 555–561