Literature Cited
A. D. Aleksandrov, Uniqueness conditions and estimates of the solutions of the Dirichlet problem, Vestnik LGU, No. 13, Issue 3, 5–30 (1963).
A. D. Aleksandrov, Certain estimates for the Dirichlet problem, DAN SSSR,134, 5, 1001–1004 (1960).
I. Ya. Bakel'man, Theory of quasi-linear elliptic equations, Sib. matem. zh.2, 2, 179–186 (1961).
A. D. Aleksandrov, Method of the reference image in the investigation of the solutions of boundary problems, Proceedings of the Soviet-American Symposium on Partial Differential Equations, Novosibirsk (1963).
A. D. Aleksandrov, Investigations on the principle of the maximum, V, Izv. vyssh. ucheb. zavedenii, No. 5 16–26 (1960).
V. G. Maz'ya, Some estimates for solutions of elliptic second-order equations, DAN SSSR,137, 5 1057–1059 (1961).
G. Stampacchia, Contributi alla regolarizzazione delle soluzioni dei problemi al contorno [Contributions to the regularization of the solutions of boundary problems], Ann. Scuola Norm. Sup. Pisa,12, 88–92 (1958).
H. G. Weinberger, Symmetrization in uniformly elliptic problems, Studies in Mathematical Analysis and Related Topics, University Press, Stanford, 424–428 (1962).
M. Frasca, Un problema variazionale per operatori ellittici [A variational problem for elliptic operators], Matematiche,18, 1–11 (1963).
S. Saks, Theory of the Integral [Russian translation], IL, Moscow (1949).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 3, pp. 486–498, May–June, 1966.
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Aleksandrov, A.D. General method for majorizing the solutions of the Dirichlet problem. Sib Math J 7, 394–403 (1966). https://doi.org/10.1007/BF00966237
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DOI: https://doi.org/10.1007/BF00966237