| Abstrakt: |
The author discovered S.L. Sobolev's spaces in the classes of potential and vortex fields introduced by H. Weyl. Let's call them Sobolev–Weyl spaces. The gradient from the divergence, the rotor and their powers are used in defining these spaces. The direct sums of these spaces form a two-parametric family (network) of Sobolev–Weyl spaces. In these spaces. we investigated boundary value problems for the gradient-of-divergence operator, rotor (curl) and their degrees with a parameter as well as the boundary value problem C for the Stokes operator. In the case when the parameter does not belong to the spectra of these operators, there are theorems for the existence and uniqueness of solutions to these problems. Otherwise, the problems are solvable according to Fredholm. Exacts a priori estimates have been obtained. [ABSTRACT FROM AUTHOR] |
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