KERNELS OF TRACE OPERATORS AND BOUNDARY VALUE PROBLEMS IN FIELD THEORY

摘要

We propose an approach to formulation and solution of a series of boundary value problems in field theory based on the use of kernels of the trace operators and functionals in Sobolev spaces. The boundary conditions are nonlocal and can contain the main first order operators (gradient, curl, and divergence) of field theory. The case of plane vector fields is separately studied.