References
Weinstein A., “Ein hydrodynamischer Unitatsatz,” Math. Z.,19, 265–274 (1924).
Leray J. andWeinstein, A., “Sur un probleme de representation conforme pose par la theorie de Helmholtz,” C. R. Acad. Sci. Paris,198, 430–433 (1934).
Leray, J., “Les problems de representation conforme de Helmholtz theorie des sillages et des proues,” Comm. Math. Helvetici,8, No. 2, 149–180; 250–263 (1935–1936).
Lavrent’ev M. A., “On some properties of univalent functions with applications to jet theory,” Mat. Sb.,4, 391–458 (1938).
Lavrent’ev M. A., “On some boundary problems in the theory of univalent functions,” Mat. Sb.,1, 815–846 (1936).
Serrin J. B., “Existence theorems for some hydrodynamical free boundary problems,” J. Rational Mech. Anal.,1, 1–48 (1952).
Lavrent’ev M. A. andShabat B. V. Hydrodynamical Problems and Their Mathematical Models [in Russian], Nauka, Moscow (1977).
Monakhov V. N., Boundary Value Problems with Free Boundaries for Elliptic Systems of Equations [in Russian], Nauka, Novosibirsk (1977).
Polubarinova-Kochina P. Ya., The Theory of Motion of Ground Waters [in Russian], GITTL, Moscow (1952).
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 5, pp. 1106–1121, September–October, 2000.
Rights and permissions
About this article
Cite this article
Monakhov, V.N. On a variational method for solving hydrodynamical free boundary problems. Sib Math J 41, 907–920 (2000). https://doi.org/10.1007/BF02674747
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674747