Literature Cited
M. Sh. Birman and M. Z. Solomyak, “Asymptotics of the spectrum of pseudodifferential operators with anisotropic, homogeneous symbols,” Vestn. Leningr. Gos. Univ., No. 13, 13–21 (1977).
B. R. Vainberg and V. V. Grushin, “On uniformly nonelliptic problems. I, II,” Mat. Sb.,72, No. 4, 602–636 (1967).; No. 1, 126–154 (1967).
R. Seeley, “The resolvent of an elliptic boundary problem,” Am. J. Math.,91, No. 4, 889–920 (1969).
L. Hörmander, “Pseudodifferential operators and nonelliptic boundary value problems,” in: Pseudodifferential Operators [Russian translation], Mir, Moscow (1967), pp. 166–296.
M. Sh. Birman and M. Z. Solomyak, “On the asymptotics of the spectrum of variational problems with differential connections,” in: Proceedings of the Conference Dedicated to the 75th Birthday of Academician I. G. Petrovskii, Moscow State Univ. (1978).
M. Z. Solomyak, “On linear elliptic systems of first order,” Dokl. Akad. Nauk SSSR,150, No. 1, 48–51 (1963).
M. Sh. Birman and M. Z. Solomyak, “Spectral asymptotics of nonsmooth elliptic operators. I,” Tr. Mosk. Mat. Obshch.,27, 3–52 (1972).
J. J. Duistermaat, Fourier Integral Operators, Academic Press, New York (1973).
G. I. Éskin, Boundary Value Problems for Elliptic Pseudodifferential Equations [in Russian], Nauka, Moscow (1973).
L. Hörmander, “Pseudodifferential operators,” in: Pseudodifferential Operators [Russian translation], Mir, Moscow (1967), pp. 63–87.
S. Sternberg, Lectures on Differential Geometry [Russian translation] Mir., Moscow (1970).
D. Fujiwara, “On the asymptotic formula for the Green operators for elliptic operators on compact manifolds,” J. Fac. Sci. Univ. Tokyo, Sec. I,14, No. 2, 251–283 (1967).
J. L. Lions and E. Magenes, Inhomogeneous Boundary Value Problems and Their Applications [Russian translation], Mir, Moscow (1971).
P. D. Lax and L. Nirenberg, “On stability for difference schemes, a sharp form of Gårding's inequality,” Commun. Pure Appl. Math.,19, No. 4, 473–492 (1966).
J. J. Kohn and L. Nirenberg, “The algebra of pseudodifferential operators,” in: Pseudodifferential Operators [Russian translation], Mir, Moscow (1967), pp. 9–62.
Yu. M. Berezanskii, Expansion in Terms of Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
M. Sh. Birman, “On the theory of self-adjoint extensions of positive definite operators,” Mat. Sb.,38, No. 4, 431–450 (1956).
M. Sh. Birman, “Perturbations of the continuous spectrum of a singular elliptic operator with variation of the boundary and the boundary conditions” Vestn. Leningr. Gos. Univ., No. 1, 22–25 (1962).
Additional information
Leningrad State University. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 1, pp. 3–22, January–February, 1979.
Rights and permissions
About this article
Cite this article
Birman, M.S., Solomyak, M.Z. Asymptotics of the spectrum of variational problems on solutions of elliptic equations. Sib Math J 20, 1–15 (1979). https://doi.org/10.1007/BF00976125
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00976125