Necessary conditions for the K-extremum of a variational functional in Sobolev spaces over multi-dimensional domains - Orlov, I.V.; Bozhonok, E.V.; Kuzmenko, E.M. (Reports of the National Academy of Sciences of Ukraine, 2014)
This paper deals with a generalized Euler–Ostrogradsky equation and necessary conditions of the Legendre type in the case of the compact extrema of variational functionals in Sobolev spaces over multidimensional domains. The inverse problem of smoothness refinement for the solutions of the generalized Euler–Ostrogradsky equation is considered. It is shown that the solution of the generalized variational Euler–Ostrogradsky equation in the Sobolev space has additional analytic properties.