In:
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Steklov Mathematical Institute, Vol. 312 ( 2021-3), p. 158-169
Abstract:
We consider a number of nonstandard boundary value problems for the system of Poisson equations on the plane. The statement of these problems is based on the decomposition of the Sobolev space into the sum of kernels of trace functionals and one-dimensional subspaces spanned by a basis vector on which the corresponding trace functional is nontrivial. These problems are nonstandard in the sense that the boundary conditions are nonlocal and may contain the main first-order differential operators of field theory, i.e., the gradient, divergence, and curl. We prove existence and uniqueness theorems for the solutions in the framework of the duality between the Sobolev space and its conjugate space.
Type of Medium:
Online Resource
ISSN:
0371-9685
Language:
Russian
Publisher:
Steklov Mathematical Institute
Publication Date:
2021
