Literature Cited
É. B. Bykhovskii and N. V. Smirnov, “Orthogonal decomposition of the space of vector functions square integrable in a given region and vector analysis operators,” Trans. of the V. A. Steklov Inst. of Math., USSR Academy of Sciences,59, 5 (1960).
M. Sh. Birman, “Maxwell operator in regions with edges,” J. Sov. Math.,37, No. 1 (1987).
M. Sh. Birman, “Maxwell operator for a resonator with reentrant edges,” Vestn. Leningr. Gos. Univ., Ser. 1, No. 3, 3 (1986).
I. S. Gudovich and S. G. Krein, “Boundary-value problems for overdetermined systems of partial differential equations,” in: Differential Equations [in Russian], No. 9, Vilnius (1974), pp. 1–146.
V. A. Kondrat'ev and O. A. Oleinik, “Boundary-value problems for partial differential equations in nonsmooth regions,” Usp. Mat. Nauk,38, 3 (1983).
V. Zaionchkovskii and V. A. Solonnikov, “Neumann problem for second-order elliptic equations with edges on a boundary,” J. Sov. Math.,27, No. 2, (1984).
V. G. Maz'ya, Sobolev Spaces [in Russian], Leningrad State Univ. (1985).
O. A. Ladyzhenskaya, Mathematical Theory of Viscous Incompressible Flow, Gordan and Breach (1969).
O. A. Ladyzhenskaya and V. A. Solonnikov, “Problems of vector analysis and generalized formulations of boundary-value problems for Navier-Stokes equations,” J. Sov. Math.,10, No. 2 (1987).
V. A. Kondrat'ev, “Boundary-value problems for elliptic equations in regions with conical or angular points,” Tr. Mosk. Mat. Ob.,16, 209 (1967).
V. A. Kondrat'ev, “Smoothness of the solution of the Dirichlet problem for a secondorder elliptic equation in the neighborhood of an edge,” Diff. Uravn.,6, 1831 (1970).
V. A. Kondrat'ev, “Aspects of the solution of the Dirichlet problem for second-order elliptic equations in the neighborhood of an edge,” Diff. Uravn.,13, 2026 (1977).
V. G. Maz'ya and B. A. Plamenevskii, “First boundary-value problem for classical equations of mathematical physics in regions with piecewise smooth boundaries. I, II,” Z. Anal. Anwendungen,2, 335, 523 (1983).
Additional information
To the memory of our teacher Leonid Vital'evich Kantorovich.
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 1, pp. 23–36, January–February, 1987.
Rights and permissions
About this article
Cite this article
Birman, M.S., Solomyak, M.Z. Maxwell operator in regions with nonsmooth boundaries. Sib Math J 28, 12–24 (1987). https://doi.org/10.1007/BF00970204
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970204