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Book Review
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Book Information
Author(s):
V. M. Filippov
Title:
Variational principles for nonpotential operators
Additional book information:
Transl. Math. Monographs, vol. 77, Amer. Math. Soc. Providence, RI, 1989, 239 pp., $99.00. ISBN 0-8218-4529-2
References:
- 1.
- F. Belatoni, Über die Charakterisierbarkeit partieller Differentialgleichungen zweiter Ordnung mit Hilfe der Variationsrechnung, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 229-233. MR 132423
- 2.
- E. T. Copson, Partial differential equations and the calculus of variations, Proc. Roy. Soc. Edinburgh 46 (1925/26), 126-135.
- 3.
- K. O. Friedrichs, Ein Verfahren der Variationsrechnung das Minimum eines Integrals als das Maximum eines anderen Ausdruckes darzustellen, Nachr. Ges. Wiss. Göttingen Math. -Phys. Kl. (1929), 13-20.
- 4.
- K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55 (1944), 132-151. MR 9701
- 5.
- D. Hilbert, Über das Dirichletsche Prinzip, Math. Ann. 59 (1904), 161-186. MR 1511266
- 6.
- B. Levi, Sul principo di Dirichlet, Rend. Circ. Mat. Palermo 6 (1906), 293-360.
- 7.
- W. V. Petryshyn, On the extension and the solution of nonlinear operator equations, Illinois J. Math. 10 (1966), 255-274. MR 208432
- 8.
- W. V. Petryshyn, Direct and iterative methods for the solution of linear operator equations in Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 675-690. MR 145651
- 9.
- V. M. Shalov, The principle of a minimum of a quadratic functional for a hyperbolic equation, Differentsial'nye Uravneniya 1 (1965), 1338-1365; English transl, in Differential Equations 1 (1965). MR 186950
- 10.
- V. M. Shalov, Solution of nonselfadjoint equations by the variational method, Dokl. Akad. Nauk SSSR 151 (1963), 511-512; English transl, in Soviet Math., Dokl. 4 (1963). MR 150597
- 11.
- M. G. Slobodyanskii, On transformation of the problem of the minimum of a functional to the problem of the maximum, Dokl. Akad. Nauk SSSR 91(1953), 733-736. MR 71869
- 12.
- S. Zaremba, Sur le principe de minimum, Bull. Int. Acad. Sci. Cracovie Cl. Sci. Math. Nat. 7 (1909), 199-264.
Additional Information:
Reviewer(s):
Roman I.
Andrushkiw
Review Information:
Journal:
Bull. Amer. Math. Soc.
25
(1991),
221-228.
DOI:
10.1090/S0273-0979-1991-16073-8
PII:
S 0273-0979(1991)16073-8
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