Bozhonok K. Compact extrema and compact analytical properties of basic variational functional in Sobolev space

The thesis is devoted to the study of compact extremums and compact-analytical properties of the basic variational functional in Sobolev space W21. The construction of the general theory of compact extremums and of compact-analytical properties of the variational functionals in Hilbert Sobolev spaces is carried out on the whole. The methods of differential equations, calculus of variations, functional analysis and infinite-dimensional mathematical analysis are applied. The sufficient conditions of well-posedness, K-continuity, K-differentiability of the variational functional in W21 are proved. The Legendre necessary condition and Legendre-Jacobi sufficient condition for K-extremum of the variational functional in W21 are obtained. The results of investigations can be used in the actual problems of modern calculus of variations which have applications in mathematical physics.