TY - INPR
A1 - Polkovnikov, Alexander
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Riemann-Hilbert problem for the Moisil-Teodorescu system
N2 - In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations
for a function u with values in 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-Lopaniskij 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.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 3
KW - Dirac operator
KW - Riemann-Hilbert problem
KW - Fredholm operators
Y1 - 2017
UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/39703
UR - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus4-397036
VL - 6
IS - 3
ER -