Geodesic
Kernels of Trace Functionals and Field-Theory Boundary Value Problems on the Plane
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 158-169

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2021_312_a7,
     author = {Yu. A. Dubinskii},
     title = {Kernels of {Trace} {Functionals} and {Field-Theory} {Boundary} {Value} {Problems} on the {Plane}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {158--169},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a7/}
}
TY  - JOUR
AU  - Yu. A. Dubinskii
TI  - Kernels of Trace Functionals and Field-Theory Boundary Value Problems on the Plane
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 158
EP  - 169
VL  - 312
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2021_312_a7/
LA  - ru
ID  - TM_2021_312_a7
ER  - 
%0 Journal Article
%A Yu. A. Dubinskii
%T Kernels of Trace Functionals and Field-Theory Boundary Value Problems on the Plane
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 158-169
%V 312
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2021_312_a7/
%G ru
%F TM_2021_312_a7
Yu. A. Dubinskii. Kernels of Trace Functionals and Field-Theory Boundary Value Problems on the Plane. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 158-169. http://geodesic.mathdoc.fr/item/TM_2021_312_a7/