On two parameter singular perturbation of linear boundary value problems
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- by W. M. Greenlee PDF
- Proc. Amer. Math. Soc. 27 (1971), 268-274 Request permission
Abstract:
A two parameter perturbation estimate for solutions of a functional equation in Hilbert space is derived. The estimate is applied to two parameter singular perturbation of elliptic boundary value problems with homogeneous Dirichlet boundary data.References
- R. Adams, N. Aronszajn, and K. T. Smith, Theory of Bessel potentials. II, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 2, 1–135 (1968). MR 228702
- N. Aronszajn and K. T. Smith, Theory of Bessel potentials. I, Ann. Inst. Fourier (Grenoble) 11 (1961), 385–475 (English, with French summary). MR 143935
- N. Aronszajn, Quadratic forms on vector spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 29–87. MR 0140920
- Avner Friedman, Singular perturbations for partial differential equations, Arch. Rational Mech. Anal. 29 (1968), 289–303. MR 226164, DOI 10.1007/BF00276729
- W. M. Greenlee, Rate of convergence in singular perturbations, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 135–191, vi (1969) (English, with French summary). MR 241795
- W. M. Greenlee, A two parameter peturbation estimate, Proc. Amer. Math. Soc. 24 (1970), 67–74. MR 284866, DOI 10.1090/S0002-9939-1970-0284866-5
- Denise Huet, Phénomènes de perturbation singulière dans les problèmes aux limites, Ann. Inst. Fourier (Grenoble) 10 (1960), 61–150 (French). MR 118968 —, Perturbations singulières et régularité, C. R. Acad. Sci. Paris, Ser A-B 266 (1968), A924-A926. MR 38 #1383. —, Perturbations singulières et régularité, C. R. Acad. Sci. Paris, Ser. A-B 266 (1968), A1237-A1239. MR 38 #1384.
- J.-L. Lions, Espaces intermédiaires entre espaces hilbertiens et applications, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine (N.S.) 2(50) (1958), 419–432 (French). MR 151829
- J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
- Robert E. O’Malley Jr., Topics in singular perturbations, Advances in Math. 2 (1968), 365–470. MR 232056, DOI 10.1016/0001-8708(68)90023-6
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 268-274
- MSC: Primary 35.45
- DOI: https://doi.org/10.1090/S0002-9939-1971-0288415-8
- MathSciNet review: 0288415