Estimation of the Kolmogorov \(N\)-widths for certain compacts in the strengthened Sobolev spaces
The author considers variational problems in unusual subsets of Sobolev spaces. Provided with special scalar products, these subsets are Hilbert spaces (so-called strenghened Sobolev spaces). In the two-dimensional case, the squared norm of an unusual subset contains integrals of squared first derivatives over segments (stringers, rods). More complex problems correspond to the equilibrium conditions for plates supported by rods or stringers. These problems were formulated (in the pre-Hilbert space) by S. P. Timoshenko in 1915. The three-dimensional problems are connected, for instance, with certain hydrodynamic problems. The author cites also examples of problems on compound manifolds including blocks of different dimensions, and gives estimations of the widths of corresponding compacts.
scientific article; zbMATH DE number 1175133