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Swetits, J.; Rogers, C.

On complementary extremum principles. (English) Zbl 0375.49019

J. Math. Anal. Appl. 62, 445-452 (1978).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0375.49019

MSC:

49S05 Variational principles of physics
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35A15 Variational methods applied to PDEs
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References:

[1] Noble, B., Complementary Variational Principles for Boundary Value Problems. I. Basic Principles with an Application to Ordinary Differential Equations, MRC Technical Summary Report No. 473 (November 1964)
[2] Rall, L. B., On complementary variational principles, J. Math. Anal. Appl., 14, 174-184 (1966) · Zbl 0135.32502
[3] Arthurs, A. M., Complementary Variational Principles (1970), Clarendon: Clarendon Oxford · Zbl 0202.38404
[4] Arthurs, A. M., Canonical approach to biharmonic variational problems, Quart. Appl. Math., 28, 135-138 (1970) · Zbl 0208.13902
[5] Arthurs, A. M., A note on Komkov’s class of boundary value problems and associated variational principles, J. Math. Anal. Appl., 33, 402-407 (1971) · Zbl 0183.39301
[6] Arthurs, A. M., Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl., 41, 781-795 (1973) · Zbl 0251.35049
[7] Arthurs, A. M., Complementary variational principles for linear equations, J. Math. Anal. Appl., 49, 237-239 (1975) · Zbl 0299.49020
[8] Noble, B.; Sewell, M. J., On dual extremum principles in applied mathematics, J. Inst. Math. Appl., 9, 123-193 (1972) · Zbl 0236.49002
[9] Wenger, N. C., A variational principle for magnetohydrodynamic channel flow, J. Fluid. Mech., 43, 211-224 (1970) · Zbl 0212.59802
[10] Smith, P., Some extremum principles for magnetohydrodynamic flow in conducting pipes, (Proc. Cambridge Philos. Soc., 72 (1972)), 303-313 · Zbl 0249.76065
[11] Smith, P., Some extremum principles for pipe flow in magnetohydrodynamics, Z. Angew. Math. Phys., 23, 753-764 (1972) · Zbl 0248.76048
[12] Sloan, D. M., Extremum principles for magnetohydrodynamic channel flow, Z. Angew. Math. Phys., 24, 689-698 (1973) · Zbl 0273.76071
[13] Chang, C. C.; Lundgren, T. S., Duct flow in magnetohydrodynamics, Z. Angew. Math. Phys., 12, 100-114 (1961) · Zbl 0115.21904
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