Geodesic
A Riemann-Hilbert problem for the Moisil--Teodorescu system
Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 155-192

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

In a bounded domain with smooth boundary in $\mathbb{R}^3$ we consider the stationary Maxwell equations for a function $u$ with values in $\mathbb{R}^3$ subject to a nonhomogeneous condition $(u,v)_x = u_0$ on the boundary, where $v$ is a given vector field and $u_0$ a function on the boundary. We specify this problem within the framework of the Riemann–Hilbert boundary value problems for the Moisil–Teodorescu system. This latter is proved to satisfy the Shapiro–Lopatinskij condition if an only if the vector $v$ is at no point tangent to the boundary. The Riemann–Hilbert problem for the Moisil–Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro–Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem. 
@article{MT_2018_21_1_a6,
     author = {A. N. Polkovnikov and N. Tarkhanov},
     title = {A {Riemann-Hilbert} problem for the {Moisil--Teodorescu} system},
     journal = {Matemati\v{c}eskie trudy},
     pages = {155--192},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2018_21_1_a6/}
}
TY  - JOUR
AU  - A. N. Polkovnikov
AU  - N. Tarkhanov
TI  - A Riemann-Hilbert problem for the Moisil--Teodorescu system
JO  - Matematičeskie trudy
PY  - 2018
SP  - 155
EP  - 192
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2018_21_1_a6/
LA  - ru
ID  - MT_2018_21_1_a6
ER  - 
%0 Journal Article
%A A. N. Polkovnikov
%A N. Tarkhanov
%T A Riemann-Hilbert problem for the Moisil--Teodorescu system
%J Matematičeskie trudy
%D 2018
%P 155-192
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2018_21_1_a6/
%G ru
%F MT_2018_21_1_a6
A. N. Polkovnikov; N. Tarkhanov. A Riemann-Hilbert problem for the Moisil--Teodorescu system. Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 155-192. http://geodesic.mathdoc.fr/item/MT_2018_21_1_a6/