The basic boundary value problems of static elasticity theory and their Cosserat spectrum
The well-known Liechtenstein's method [\textit{L. Liechtenstein}, Math. Z. 20, 21-28 (1924)] of reducing the first basic boundary problem of static elasticity theory (BPET) to equivalent integral Fredholm equation of the second kind on the boundary is extended to all the rest BPET (the second, third and fourth). The Cosserat spectra of all four BPET's are also studied, and the asymptotics of finite-multiple eigenvalues tending to a unique limiting point \(-2\), 0, \(-1\) or \(-1\) are obtained for the first, second, third or fourth BPET, respectively. For the Stokes problem from hydromechanics (linearized stationary Navier- Stokes equation), we prove the convergence in Sobolev space of a new iteration algorithm for construction of the solution; this algorithm is much better than the known algorithm by Uzawa and Arrow-Hurwicz.
scientific article; zbMATH DE number 549771
scientific article