On an oblique derivative problem involving an indefinite weight
Archivum mathematicum, Tome 30 (1994) no. 4, pp. 237-262 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we derive results concerning the angular distrubition of the eigenvalues and the completeness of the principal vectors in certain function spaces for an oblique derivative problem involving an indefinite weight function for a second order elliptic operator defined in a bounded region.
In this paper we derive results concerning the angular distrubition of the eigenvalues and the completeness of the principal vectors in certain function spaces for an oblique derivative problem involving an indefinite weight function for a second order elliptic operator defined in a bounded region.
Classification : 35J25, 35P05, 35P10
Keywords: oblique derivative; elliptic problem; indefinite weight; eigenvalues; principal vectors
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Faierman, M. On an oblique derivative problem involving an indefinite weight. Archivum mathematicum, Tome 30 (1994) no. 4, pp. 237-262. http://geodesic.mathdoc.fr/item/ARM_1994_30_4_a1/

[1] Adams, R. A.: Sobolev Spaces. Academic, New York (1975). | MR | Zbl

[2] Agmon, S.: On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems. Comm. Pure Appl. Math. 15 (1962), 119-147. | MR | Zbl

[3] Agmon, S.: Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton, N.J. (1965). | MR | Zbl

[4] Agmon, S., Douglis, A. and Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math. 12 (1959), 623-727. | MR

[5] Agranovitch, M. S., Vishik, M. I.: Elliptic problems with a parameter and parabolic problems of general type. Russian Math. Surveys 19 (1964), 53-157. | MR

[6] Beals, R.: Indefinite Sturm–Liouville problems and half–range completeness. J. Differential Equations 56 (1985), 391-407. | MR | Zbl

[7] Bers, L., Schechter, M.: Elliptic Equations. In: Partial Differential Equations, Lectures in Appl. Math.III, Interscience, New York, 1964, 131-299. | MR

[8] Bognár, J.: Indefinite Inner Product Spaces. Springer, New York, 1974. | MR

[9] Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw–Hill, New York, 1955. | MR

[10] Faierman, M.: On the eigenvalues of nonselfadjoint problems involving indefinite weights. Math. Ann. 282 (1988), 369-377. | MR | Zbl

[11] Faierman, M.: Elliptic problems involving an indefinite weight. Trans. Amer. Math. Soc. 320 (1990), 253–279. | MR | Zbl

[12] Faierman, M.: Non–selfadjoint elliptic problems involving an indefinite weight. Comm. Partial Differential Equations 15 (1990), 939–982. | MR | Zbl

[13] Faierman, M.: An oblique derivative problem involving an indefinite weight. Dekker, New York, 1991, 147-154, In: Differential Equations, Lecture Notes in Pure and Appl. Math. 127. | MR | Zbl

[14] Faierman, M.: An elliptic boundary value problem in a half–space. Boll. Un. Mat. Ital. 5-B (1991), 905-937. | MR | Zbl

[15] Faierman, M.: Generalized parabolic cylinder functions. Asymptotic Anal. 5 (1992), 517-531. | MR | Zbl

[16] Faierman, M.: A priori bounds for solutions of an elliptic equation. Proc. Roy. Soc. Edinburgh (to appear). | MR | Zbl

[17] Fleckinger, J., Lapidus, M. L.: Eigenvalues of elliptic boundary value problems with an indefinite weight function. Trans. Amer. Math. Soc. 295 (1986), 305-324. | MR

[18] Fleckinger, J., Lapidus, M. L.: Remainder estimates for the asymptotics of elliptic eigenvalue problems with indefinite weights. Arch. Rational Mech. Anal. 98 (1987), 329-356. | MR

[19] Hess, P.: On the relative completeness of the generalized eigenvectors of elliptic eigenvalue problems with indefinite weight functions. Math. Ann. 270 (1985), 467-475. | MR | Zbl

[20] Hess, P.: On the asymptotic distribution of eigenvalues of some non–selfadjoint problems. Bull. London Math. Soc. 18 (1986), 181-184. | MR

[21] Hess, P.: On the spectrum of elliptic operators with respect to indefinite weights. Linear Algebra Appl. 84 (1986), 99-109. | MR | Zbl

[22] Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. Partial Differential Equations 8 (1983), 21-64. | MR

[23] Kato, T.: Perturbation Theory for Linear Operators. 2nd edn., Springer, New York, 1976. | MR | Zbl

[24] Lions, J. L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Springer, New York, 1972. | MR

[25] Markus, A. S.: Introduction to the Spectral Theory of Polynomial Operator Pencils. Amer. Math. Soc., Providence, R.I. (1988). | MR | Zbl

[26] Schechter, M.: General boundary value problems for elliptic partial differential equations. Comm. Pure Appl. Math. 12 (1959), 457-482. | MR | Zbl

[27] Whittaker, E. T., Watson, G. N.: A Course of Modern Analysis. 4th edn., University Press, Cambridge, 1965. | MR