References
- Slavin IV, Smirnov G. Strong ellipticity for hybrid formulation of an electromagnetic diffraction problem. Comput. Math. Math. Phys. 2000;40:286–299. Russian.
- Gokhberg IT, Feldman IA. Convolution equations and projection methods for their solution. Providence (RI): American Mathematical Society; 1974. (Translations of mathematical monographs; vol. 41). 261 p.
- Birman MSh and Solomyak MZ. l\textsubscript{2}-theory of the Maxwell operator in arbitrary domains. Russ. Math. Surv. 1987;42:75–96.
- Costabel M. A coercive bilinear form for Maxwell’s equations. J. Math. Anal. Appl. 1991;157:527–541.
- Samokhin AB. Integral equations and iteration methods in electromagnetic scattering. Utrecht: De Gruyter; 2001.
- Valovik DV, Smirnov G. Method of pseudodifferential operators for a study of a volume singular integral equation. Izv. Vyssh. Uchebn. Zaved. Povolzh. Region. Fiz.-Mat. Nauki [University proceedings. Volga region. Physical and mathematical sciences. Mathematics]. 2009:102–114.
- Valovik DV, Smirnov YuG. Pseudodifferential operator method in a problem on the diffraction of an electromagnetic wave on a dielectric body. Differ. Equ. 2012;48:517–523.
- Samokhin AB. Volume singular integral equations for problems of scattering on three-dimensional dielectric structures. Differ. Equ. 2014;50:1201–1216.
- Costabel M, Darrigand E, Koné EH. Volume and surface integral equations for electromagnetic scattering by a dielectric body. J. Comput. Appl. Math. 2010;234:1817–1825.
- Ilynsky AS, Kravtsov VV, Sveshnikov AG. Mathematical models in electromagnetics. Moscow: Vysshaya Shkola; 1991. Russian.
- Smirnov YuG, Tsupak AA. Integro-differential equations of the vector problem of electromagnetic wave diffraction by a system of nonintersecting screens and inhomogeneous bodies. Adv. Math. Phys. 2015;2015:1–6.
- Vladimirov VS. Equations of mathematical physics. New York (NY): Marcel Dekker; 1971.
- Colton DL, Kress R. Integral equation methods in scattering theory. New York (NY): John Wiley & Sons Inc.; 1983.
- Mikhlin SG. Multidimensional singular integrals and integral equations. Oxford: Pergamon Press; 1965.
- Kobayashi K, Shestopalov YuV, Smirnov YuG. Investigation of electromagnetic diffraction by a dielectric body in a waveguide using the method of volume singular integral equation. SIAM J. Appl. Math. 2009;70:969–983.
- Egorov V, Shubin MA. Partial differential equations II elements of the modern theory. Equations with constant coefficients. Vol. 31, Encyclopaedia of mathematical sciences. Berlin: Springer; 1994.
- Shubin MA. Pseudodifferential operators and spectral theory. Berlin: Springer-Verlag; 2001.
- Rempel S, Schulze B-W. Index theory of elliptic boundary problems. Berlin: Akademie-Verlag; 1982.
- Kato T. Perturbation theory for linear operators. Heidelberg: Springer; 1966.
- Egorov V. Lectures on partial differential equations: supplementary chapters. Moscow: Moscow University Press; 1985. Russian.
- Triebel H. Theory of function spaces. Basel: Birkhäuser; 1983.
- Bychovskii EB, Smirnov NV. On the orthogonal decomposition of a space of vector-functions which are square-summable over a prescribed domain and operators of vector analysis. Proc. Steklov Inst. Math. 1960;59:5–36.
- Costabel M. A remark on the regularity of solutions of Maxwell’s equations on lipschitz domains. Math. Methods Appl. Sci. 1990;12:365–368.
- Ladyzhenskaya OA, Ural NN. Linear and quasilinear elliptic equations. Moscow: Nauka; 1964. Russian.
- Ladyzhenskaya OA, Ural’tseva NN. Linear and quasilinear elliptic equations. New York (NY): Academic Press; 1968.
- Ilynsky AS, Smirnov YuG. Electromagnetic wave diffraction by conducting screens: pseudodifferential operators in diffraction problems. Utrecht: VSP; 1998.
- Lions JL, Magenes E. Non-homogeneous boundary value problems and applications. Vol. 181, Grundlehren der mathematischen Wissenschaften Springer-Verlag: Berlin; 1972.
- Taylor ME. Pseudodifferential operators. Princeton (NJ): Princeton University Press; 1981.
- Mizohata S. The theory of partial differential equations. Cambridge: Cambridge University Press; 1973.
- Courant R, Hilbert D. Methods of mathematical physics. Vol. 2, New York (NY): Wiley-VCH; 1989.