References
Cesari L., Existence theorems for optimal solutions in Pontryagin and Lagrange problems. SIAM J. Control 3, 475–498 (1966).
Cesari L., Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints, I and II. Trans. Amer. Math. Soc. 124, 369–412, 413–429 (1966).
Cesari L., Existence Theorems for Multidimensional Problems of Optimal Control. Differential Equations and Dynamical Systems (J. K. Hale and J. P. La Salle editors), 115–132. Academic Press 1967.
Cesari L., Existence theorems for multidimensional Lagrange problems. Journal of Optimization Theory and Applications 1, 87–112 (1967).
Cesari L., Sobolev spaces and multidimensional Lagrange problems of optimization. Annali Scuola Normale Sup. Pisa. (To appear.)
Lurie K. A., The Mayer-Bolza problem for multiple integrals and the optimization of the performance of systems with distributed parameters. Prikl. Mat. Mek. 27, 842–853 (1963). English Translation, PMM, Pergamon Press 27, 1284–1299 (1963).
Lurie K. A., Optimum control of conductivity of a fluid moving in a channel in a magnetic field. Prikl. Mat. Mek. 28, 258–267 (1964). English Translation, PMM, Pergamon Press 28, 316–327 (1964).
Lurie K. A., The Mayer-Bolza Problem for Multiple Integrals: Some Optimum Problems for Elliptic Differential Equations Arising in Magnetohydrodynamics. Topics in Optimization, pp. 147–193 (edit. G. Leitmann). Academic Press 1967.
Rashevsky P. K., Geometricheskaya Teoria Uravnenii Tchastnimi Proisvodnimi (Geometrical Theory of Partial Differential Equations). Gostekhizdat, Moscow 1947.
Thomas T. Y., & E. W. Titt, Systems of Partial Differential Equations and their Characteristic Surfaces. Ann. of Math. (2) 33, 1–80 (1932).
Cowling T. G., Magnetohydrodynamics. New York: Wiley (Interscience) 1957.
Author information
Authors and Affiliations
Additional information
Research partially supported by AF-OSR grant 942-65 at the University of Michigan. This paper was written during the author's stay at the “Institut Henri Poincaré”, Paris, Spring 1967.
Rights and permissions
About this article
Cite this article
Cesari, L. Multidimensional Lagrange problems of optimization in a fixed domain and an application to a problem of magnetohydrodynamics. Arch. Rational Mech. Anal. 29, 81–104 (1968). https://doi.org/10.1007/BF00281359
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281359