Geodesic
Integral Equations Method and the Transmission Problem for the Stokes System
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 1, p. 53

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The transmission problem for the Stokes system is studied: $\Delta{\mathbf v}_\pm=\nabla p_\pm$, $\nabla\cdot{\mathbf v}_\pm=0$ in $G_\pm$, ${\mathbf v}_+-{\mathbf v}_-={\mathbf g}$, $a_+T({\mathbf v}_+,p_+)\mathbf n-a_-T({\mathbf v}_-,p_-)\mathbf n=\mathbf f$ on $\partial G_+$. Here $G_+\subset R^3$ is a bounded open set with Lipschitz boundary and $G_-$ is the corresponding complementary open set. Using the integral equation method we study the problem in homogeneous Sobolev spaces. Under assumption that $\partial G_+$ is of class ${\cal C}^1$ we study this problem also in Besov spaces and $L^q$-solutions of the problem. We show the unique solvability of the problem. Moreover, we solve the corresponding boundary integral equations by the successive approximation method.
Classification : 35Q35 65N38
Keywords: transmission problem, Stokes system, integral equation method 
@article{KJM_2015_39_1_a5,
     author = {D. Medkov\'a},
     title = {Integral {Equations} {Method} and the {Transmission} {Problem} for the {Stokes} {System}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {53 },
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a5/}
}
TY  - JOUR
AU  - D. Medková
TI  - Integral Equations Method and the Transmission Problem for the Stokes System
JO  - Kragujevac Journal of Mathematics
PY  - 2015
SP  - 53 
VL  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a5/
LA  - en
ID  - KJM_2015_39_1_a5
ER  - 
%0 Journal Article
%A D. Medková
%T Integral Equations Method and the Transmission Problem for the Stokes System
%J Kragujevac Journal of Mathematics
%D 2015
%P 53 
%V 39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a5/
%G en
%F KJM_2015_39_1_a5
D. Medková. Integral Equations Method and the Transmission Problem for the Stokes System. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 1, p. 53 . http://geodesic.mathdoc.fr/item/KJM_2015_39_1_a5/