Critical points on closed elliptic affine subspaces
HTML articles powered by AMS MathViewer
- by Robert Delver PDF
- Proc. Amer. Math. Soc. 51 (1975), 385-392 Request permission
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
- Felix E. Browder, Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965), 176–183. MR 179459, DOI 10.1090/S0002-9904-1965-11275-7
- Felix E. Browder, Remarks on the direct method of the calculus of variations, Arch. Rational Mech. Anal. 20 (1965), 251–258. MR 187122, DOI 10.1007/BF00253135
- Robert Delver, Variational problems within the class of solutions of a partial differential equation, Trans. Amer. Math. Soc. 180 (1973), 265–289. MR 320856, DOI 10.1090/S0002-9947-1973-0320856-9
- Robert Delver, Boundary and interior control for partial differential equations, Canadian J. Math. 27 (1975), 200–217. MR 365286, DOI 10.4153/CJM-1975-025-6 —, Elliptic variational problems. II, Lecture Notes, Rijksuniversiteit Groningen, 1974. (Available on request.)
- Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088 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.
- 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
- Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
- R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165–172. MR 158411, DOI 10.1090/S0002-9904-1964-11062-4
- Jacob T. Schwartz, Generalizing the Lusternik-Schnirelman theory of critical points, Comm. Pure Appl. Math. 17 (1964), 307–315. MR 166796, DOI 10.1002/cpa.3160170304
- Kôsaku Yosida, Functional analysis, 4th ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag, New York-Heidelberg, 1974. MR 0350358
Additional Information
- © Copyright 1975 American Mathematical Society
- 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