Abstract
Under minimal requirements on the coefficients and the boundary of the domain it is proved that the spectrum of the first boundary-value problem for an elliptic operator of second order always lies in the half-plane λ′ ≤ Re λ, where λ′ is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. On the line Re λ = λ′, there are no other points of the spectrum.
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A. G. Aslanyan and V. B. Lidskii, “On the spectrum of elliptic equations,” Matem. Zametki,7, No. 4, 495–502 (1970).
M. A. Krasnosel'skii and P. E. Sobolevskii, “On the nonnegative eigenfunction of the first boundary-value problem for an elliptic equation,” Usp. Mat. Nauk,16, No. 1, 197–199 (1961).
M. V. Keldysh, “On the solvability and stability of the Dirichlet problem,” Usp. Mat. Nauk,8, 171–231 (1941).
A. A. Novruzov, “On the regularity of boundary points for an elliptic equation with continuous coefficients,” Vestnik Moskov. Gos. Univ., Ser. Mat. i Mekh., No. 6, 18–25 (1971).
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Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 351–358, September, 1976.
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Kerimov, T.M., Kondrat'ev, V.A. The spectrum of an elliptic operator of second order. Mathematical Notes of the Academy of Sciences of the USSR 20, 756–760 (1976). https://doi.org/10.1007/BF01097244
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DOI: https://doi.org/10.1007/BF01097244