Higher-order degenerate elliptic equations: spaces, operators and boundary value problems

One gives a survey and one presents the method of the reduction of a general boundary-value problem to a Dirichlet type problem, based on the systematic use of the concept of a weighted pseudodifferential operator. One gives the fundamental results in the theory of weighted spaces of functions. The survey is compiled on the basis of the publications refereed during 1970–1983 in the Referativnyi Zhurnal “Matematika” and on the basis of the latest results published in the form of reports or preprints or deposited at VINITI.