Certain problems of vector analysis

In the paper one gives an explicit method of constructing in the domain ^m m2 a vector field, having a prescribed divergencef in and taking prescribed values on the boundary . The differential properties of the field are faithfully determined by the smoothness off, and Simultaneously, one constructs the solutions of a series of other problems of vector analysis, which present an independent interest.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 138, pp. 65–85, 1984.