On a minimization of the First Eigenvalue of the Laplace Operator over Domains

The problem of minimization of the first eigon \ alue of Laplace operator over domains is considered in present paper. For t; o solving" of this problem the given by authors definition of the variation <•' the domain is used. The numerical algorithm is proposed for the solving of his problem in general case. The finding of the first eigenvalue plays an important ro! • in the spectral theory of operators. The minimization of this eigenvalue gres possibility to provide the stability and improve some characteristics of th< system. But, the solving of the control problem over domains meets some dii iculities related with the variation of the domain.