Olga Arsenievna Oleinik (Russian: О́льга Арсе́ньевна Оле́йник) (2 July 1925 – 13 October 2001) was a Soviet mathematician who conducted pioneering work on the theory of partial differential equations, the theory of strongly inhomogeneous elastic media, and the mathematical theory of boundary layers. She was a student of Ivan Petrovsky. She studied and worked at the Moscow State University.
She received many prizes for her remarkable contributions: the Chebotarev Prize in 1952; the Lomonosov Prize in 1964; the State Prize 1988; the Petrowsky Prize in 1995; and the Prize of the Russian Academy of Sciences in 1995. Also she was member of several foreign academies of sciences, and earned several honorary degrees.
On May 2, 1985 Olga Oleinik was awarded the laurea honoris causa by the Sapienza University of Rome, jointly with Fritz John.
She authored more than 370 mathematical publications and 8 monographs, as the sole author or in collaboration with others: her work covers algebraic geometry, the theory of partial differential equations where her work enlightened various aspects, elasticity theory and boundary layers theory.
She was an enthusiast and very active teacher, advising the thesis of 57 "candidates".
Oleinik, Olga A. (1957), "Discontinuous solutions of non-linear differential equations", Uspekhi Matematicheskikh Nauk (in Russian), 12 (3(75)): 3–73, MR 94541, Zbl 0080.07701 . An important paper where the author describes generalized solutions of nonlinear partial differential equations as BV functions.Oleinik, Olga A. (1959), "Construction of a generalized solution of the Cauchy problem for a quasi-linear equation of first order by the introduction of "vanishing viscosity"", Uspekhi Matematicheskikh Nauk (in Russian), 14 (2(86)): 159–164, MR 117426, Zbl 0096.06603 . An important paper where the author constructs a weak solution in BV for a nonlinear partial differential equation with the method of vanishing viscosity.Oleinik, O. A. (1960), "A method of solution of the general Stefan problem", Doklady Akademii Nauk SSSR (in Russian), 135: 1050–1057, Zbl 0131.09202 . An important paper in the theory of the Stefan problem: generalizing earlier work of her doctoral student S. L. Kamenomostskaya, the author proves the existence of a generalized solution for the multi dimensional model.Oleinik, Olga A.; Radkevich, Evgenii V. (1973), Second order equations with nonnegative characteristic form, New York and London / Providence, R.I.: Plenum Press / AMS, pp. vii+259, ISBN 0-306-30751-0, MR 457907, Zbl 0217.41502 (reviews of the Russian edition).Oleinik, Olga Arsenievna; Kondratiev, Vladimir Alexandrovitch (1989), "On Korn's inequalities", Comptes rendus hebdomadaires des séances de l'Académie des Sciences, Série I: Mathématiques, 308 (16): 483–487, MR 0995908, Zbl 0698.35067 .Cioranescu, Doina; Oleinik, Olga Arsenievna; Tronel, Gérard (1989), "On Korn's inequalities for frame type structures and junctions", Comptes rendus hebdomadaires des séances de l'Académie des Sciences, Série I: Mathématiques, 309 (9): 591–596, MR 1053284, Zbl 0937.35502 .Oleinik, O. A.; Shamaev, A. S.; Yosifian, G. A. (1991), Mathematical problems in elasticity and homogenization, Studies in Mathematics and its Applications, 26, Amsterdam – London – New York – Tokyo: North-Holland, pp. xiv+398, ISBN 0-444-88441-6, MR 1195131, Zbl 0768.73003 .Oleinik, Olga A. (1992), "Korn's Type inequalities and applications to elasticity", in Amaldi, E.; Amerio, L.; Fichera, G.; Gregory, T.; Grioli, G.; Martinelli, E.; Montalenti, G.; Pignedoli, A.; Salvini, Giorgio; Scorza Dragoni, Giuseppe, Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990), Atti dei Convegni Lincei (in Italian), 92, Roma: Accademia Nazionale dei Lincei, pp. 183–209, ISSN 0391-805X, MR 1783034, Zbl 0972.35013. .Kozlov, S. M.; Oleinik, O. A.; Zhikov, V. V. (1994), Homogenization of differential operators and integral functionals, Berlin-Heidelberg-New York: Springer-Verlag, pp. xii+570, ISBN 3-540-54809-2, MR 1329546, Zbl 0838.35001 .Oleinik, O. A.; Samokhin, V. N. (1999), Mathematical models in boundary layer theory, Applied Mathematics and Mathematical Computation, 15, London-Weinheim-New York-Tokyo-Melbourne-Madras: Chapman & Hall/CRC Press, pp. x+516, ISBN 1-58488-015-5, MR 1697762, Zbl 0928.76002 .