Carleman formula for the Maxwell equation in a cap type domain
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 317-322.

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

We consider a Cauchy problem for the Maxwell equations in a cap type domain $\mathcal{X}$ in $\mathbb{R}^3$. We find reasonable solvability conditions and a Carleman formula for its solution.
Keywords: scattering, elliptic complex, Green formulas, Stratton–Chu formulas, Cauchy problem.
Mots-clés : Carleman formula
@article{JSFU_2019_12_3_a5,
     author = {Komil O. Makhmudov},
     title = {Carleman formula for the {Maxwell} equation in a cap type domain},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {317--322},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a5/}
}
TY  - JOUR
AU  - Komil O. Makhmudov
TI  - Carleman formula for the Maxwell equation in a cap type domain
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 317
EP  - 322
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a5/
LA  - en
ID  - JSFU_2019_12_3_a5
ER  - 
%0 Journal Article
%A Komil O. Makhmudov
%T Carleman formula for the Maxwell equation in a cap type domain
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 317-322
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a5/
%G en
%F JSFU_2019_12_3_a5
Komil O. Makhmudov. Carleman formula for the Maxwell equation in a cap type domain. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 317-322. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a5/

[1] L.A. Aizenberg, N.N. Tarkhanov, “Conditionally stable problems and Carleman formulas”, Siberian Math. J., 31:6 (1990), 9–15 | MR

[2] L.A. Aizenberg, Carleman's Formulas in Complex Analysis. Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1993 | MR

[3] D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Heidelberg, 1998 | MR | Zbl

[4] K. Makhmudov, O. Makhmudov, N. Tarkhanov, “Equations of Maxwell type”, J. Math. Anal. Appl., 378:1 (2011), 64–75 | DOI | MR | Zbl

[5] A. Shlapunov, Green's Integrals and Their Applications to Elliptic systems, Tesi di perfezionamento, Scuola Normale Superiore, Pisa, 1996

[6] A. Shlapunov, N. Tarkhanov, “Bases with double orthogonality in the Couchy problem for systems with injective symbols”, Proc. Londom Math. Soc., 71:1 (1995), 1–52 | MR | Zbl

[7] J.A. Stratton, Electromagnetic Theory, McGraw-Hill, NY, 1941 | Zbl

[8] N. Tarkhanov, Complexes of Differential Operators, Kluwer Academic Publishers, Dordrecht, NL, 1995 | MR | Zbl

[9] N. Tarkhanov, The Cauchy Problem for Solutions of Elliptic Equations, Akademie Verlag, Berlin, 1995 | MR | Zbl

[10] Sh. Yarmukhamedov, “The Cauchy problem for the Laplace equation”, Soviet Math. Dokl., 18:4 (1977), 939–942 | Zbl