Literature Cited
A. Ulam, Unsolved Mathematical Problems [Russian translation], Nauka, Moscow (1964).
S. L. Sobolev, Equations of Mathematical Physics [in Russian], 4th ed., Nauka, Moscow (1966).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], 4th ed., Nauka, Moscow (1972).
A. N. Tikhonov, “On methods for regularizing optimal control problems,” Dokl. Akad. Nauk SSSR,162, No. 4, 763 (1965).
S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1978).
I. V. Skrypnik, Nonlinear Higher-Order Elliptic Equations [in Russian], Naukova Dumka, Kiev (1973).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
Yu. N. Voinov, “Boundedness near the boundary of the gradients of generalized solutions of boundary-value problems for quasilinear elliptic equations,” Vestn. Leningr. Gos. Univ.,2, No. 7, 5–13 (1974).
M. A. Lavrent'ev and L. A. Lyusternik, Foundations of Variational Calculus [in Russian], Vol. 1, Part 2, ONTI, Moscow-Leningrad (1935).
G. H. Hardy, Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1952).
N. A. Bobylev, “On a problem of Ulam,” Dokl. Akad. Nauk SSSR,255, No. 6, 1292–1295 (1980).
M. A. Krasnosel'skii, N. A. Bobylev, and É. M. Mukhamadiev, “On a scheme for investigating degenerate extremals of functionals of classical variational calculus,” Dokl. Akad. Nauk SSSR,240, No. 3, 8–12 (1978).
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Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 4, pp. 11–21, July–August, 1985.
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Bobylev, N.A. Stability of classical solutions of variational problems of mathematical physics. Sib Math J 26, 485–493 (1985). https://doi.org/10.1007/BF00971295
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DOI: https://doi.org/10.1007/BF00971295