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Critical points on closed elliptic affine subspaces


Author: Robert Delver
Journal: Proc. Amer. Math. Soc. 51 (1975), 385-392
MSC: Primary 58E15; Secondary 49B25
DOI: https://doi.org/10.1090/S0002-9939-1975-0375385-0
MathSciNet review: 0375385
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Abstract: The critical points of a function restricted to the solution set of a linear elliptic equation are characterized. An extension of the Lagrange multiplier method is given. Existence and the relation to elliptic eigenvalue problems are discussed.


References [Enhancements On Off] (What's this?)

  • [1] F. E. Browder, Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965), 176-183. MR 31 #3707. MR 0179459 (31:3707)
  • [2] -, Remarks on the direct method of the calculus of variations, Arch. Rational Mech. Anal. 20 (1965), 251-258. MR 32 #4576. MR 0187122 (32:4576)
  • [3] R. Delver, Variational problems within the class of solutions of a partial differential equation, Trans. Amer. Math. Soc. 180 (1973), 265-289. MR 0320856 (47:9389)
  • [4] -, Boundary and interior control for partial differential equations, Canad. J. Math. 27 (1975), 200-217. MR 0365286 (51:1539)
  • [5] -, Elliptic variational problems. II, Lecture Notes, Rijksuniversiteit Groningen, 1974. (Available on request.)
  • [6] A. Friedman, Partial differential equations, Holt, Rinehart and Winston, New York, 1969. MR 0445088 (56:3433)
  • [7] J.-L. Lions, Controle optimal de systèmes gouvernés par des équations aux dérivées partielles, Dunod; Gauthier-Villars, Paris, 1968; English transl., Die Grundlehren der math. Wissenschaften, Band 170, Springer-Verlag, Berlin and New York, 1971. MR 39 #5930; MR 42 #6395.
  • [8] J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. I, Travaux et Recherches Mathématiques, no. 17, Dunod, Paris, 1968. MR 40 #512. MR 0247243 (40:512)
  • [9] C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der math. Wissenschaften, Band 130, Springer-Verlag, New York, 1966. MR 34 #2380. MR 0202511 (34:2380)
  • [10] R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165-172. MR 28 #1634. MR 0158411 (28:1634)
  • [11] J. T. Schwartz, Generalizing the Lusternik-Schnirelman theory of critical points, Comm. Pure Appl. Math. 17 (1964), 307-315. MR 29 #4069. MR 0166796 (29:4069)
  • [12] K. Yosida, Functional analysis, 3rd ed., Springer-Verlag, New York, 1971. MR 0350358 (50:2851)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0375385-0
Keywords: Variational problems, critical points, Lagrange multipliers, variational adjoint, elliptic boundary control problems, elliptic operator-eigenvalue problems
Article copyright: © Copyright 1975 American Mathematical Society

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