Olga Oleinik

Olga Arsenievna Oleinik (also as Oleĭnik) HFRSE (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.

Olga Arsenievna Oleinik
Olga Arsenievna Oleinik in Nice, 1970
Born	(1925-07-02)2 July 1925 Matusiv, Shpola Raion, Ukrainian SSR, Soviet Union
Died	13 October 2001(2001-10-13) (aged 76) Moscow, Russia
Nationality	Soviet
Alma mater	Moscow State University, 1954 (PhD)
Known for	Theory of elasticity, partial differential equations, boundary layer theory, weak solutions of nonlinear differential equations
Awards	1952 Chebotarev Prize, 1988 USSR State Prize, 1995 Petrowsky Prize, Prize of the Russian Academy of Sciences
Scientific career
Fields	Mathematics
Institutions	Moscow State University
Doctoral advisor	Ivan Petrovsky

She received many prizes for her remarkable contributions: the Chebotarev Prize in 1952; 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.

Life

On 2 May 1985 Olga Oleinik was awarded the laurea honoris causa by the Sapienza University of Rome, jointly with Fritz John.^[1]

Work

Research activity

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.

Teaching activity

She was an enthusiast and very active teacher, advising the thesis of 57 "candidates".

Selected publications of Olga Oleinik

• Oleinik, Olga A. (1957), "Discontinuous solutions of non-linear differential equations", Uspekhi Matematicheskikh Nauk (in Russian), 12 (3(75)): 3–73, MR 0094541, 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 0117426, 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, MR 0125341, 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 0457907, 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, vol. 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 (eds.), , Atti dei Convegni Lincei (in Italian), vol. 92, Roma: Accademia Nazionale dei Lincei, pp. 183–209, ISSN 0391-805X, MR 1783034, Zbl 0972.35013, archived from the original on 7 January 2017, retrieved 27 July 2014.
• 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, doi:10.1007/978-3-642-84659-5, 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, vol. 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.

See also

• Boundary layer
• Bounded variation
• Elasticity theory
• Homogenization
• Partial differential equations
• Stefan problem
• Weak solutions

Notes

1. See (Vernacchia-Galli 1986, pp. 845–855).

References

Biographical and general references

• Colautti Fichera, Matelda (December 2006), ... ed è subito sera... La lunga, brevissima vita di Gaetano Fichera (The long, extremely short life of Gaetano Fichera) (in Italian), Roma: Self-published, p. 217. The story of the life of Gaetano Fichera written by his wife, Matelda Colautti Fichera: this reference is important for understanding the friendship between Olga Oleinik, Gaetano Fichera and his wife.
• Friedlander, Susan; Keyfitz, Barbara (2006), "Olga Ladyzhenskaya and Olga Oleinik: Two Great Women Mathematicians of the 20th Century" (PDF), in Kuperberg, Krystyna (ed.), Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik – May 18–20, 2006, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. Some recollections of the authors about Olga Ladyzhenskaya and Olga Oleinik.
• Jäger, Willi; Lax, Peter; Synge Morawetz, Cathleen (2003), "Olga Arsen'evna Oleĭnik (1925–2001)" (PDF), Notices of the American Mathematical Society, 50 (2): 220–223, MR 1951108, Zbl 1159.01335. An ample commemorative paper written by three friends/collaborators.
• Magenes, E. (1996), "On the scientific work of Olga Oleinik" (PDF), Rendiconti di Matematica e delle Sue Applicazioni, Serie VII, 16 (3): 347–373, MR 1422388, Zbl 0861.35002, from the original on 28 May 2003 (Also available at the Internet Archive).
• Nirenberg, Louis (March 2004), "About Olga Arsen'evna Oleinik", Journal of Mathematical Sciences, 120 (3): 1241, doi:10.1023/B:JOTH.0000016045.00993.ef, MR 2085177, S2CID 119428680, Zbl 1290.35002. A short obituary notice by Louis Nirenberg.
• Synge Morawetz, Cathleen (2006), "Early Memories of Olga Ladyzhenskaya and Olga Oleinik" (PDF), in Kuperberg, Krystyna (ed.), Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik – May 18–20, 2006, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. Some recollections of the author about Olga Ladyzhenskaya and Olga Oleinik.
• Venttsel', T. D.; Vladimirov, V. S.; Zhikov, V. V.; Il'in, A. M.; Il'in, V. P.; Kondrat'ev, V. A.; Kudryavtsev, L. D.; Mishchenko, E. F.; Nikol'skii, S. M.; Osipov, Yu. S.; Radkevich, E. V.; Rozov, N. Kh.; Sadovnichii, V. A.; Faddeev, L. D.; Chechkin, G. A.; Shamaev, A. S.; Shaposhnikova, T. A.; Shkalikov, A. A. (2003), "Ol'ga Arsen'evna Oleinik (obituary)", Uspekhi Matematicheskikh Nauk, 58 (1(349)): 165–174, Bibcode:2003RuMaS..58..161V, doi:10.1070/RM2003v058n01ABEH000607, MR 1992133, Zbl 1050.01527. An almost comprehensive obituary article: its English translation is published in the Russian Mathematical Surveys as Ventsel, T D (2003), "Ol'ga Arsen'evna Oleinik", Russian Mathematical Surveys, 58 (1): 161–172, doi:10.1070/RM2003v058n01ABEH000607, MR 1992133, Zbl 1050.01527.
• Vernacchia-Galli, Jole (1986), "Olga Arsenievna Oleinik", Regesto delle lauree honoris causa dal 1944 al 1985, Studi e Fonti per la storia dell'Università di Roma (in Italian), vol. 10, Roma: Edizioni Dell'Ateneo, pp. 845–855. The "regest of honoris causa degrees from 1944 to 1985" (English translation of the title) is itself a detailed and carefully commented regest of all the documents of the official archive of the Sapienza University of Rome pertaining to the honoris causa degrees awarded or not. It includes all the awarding proposals submitted during the considered period, detailed presentations of the work of the candidate, if available, and precise references to related articles published on Italian newspapers and magazines, if the laurea was awarded.

Scientific references

• Radkevich, E. V. (2009), "Equations with nonnegative characteristic form. I", Journal of Mathematical Sciences, 158 (3): 297–452, doi:10.1007/s10958-009-9394-2, MR 2675370, S2CID 122736904, Zbl 1200.35158. This monograph consists of two volumes and is devoted to second-order partial differential equations (mainly, equations with nonnegative characteristic form). A number of problems of qualitative theory (for example, local smoothness and hypoellipticity) are presented, and the work of many contributors, like Olga Oleinik, Gaetano Fichera, the Author himself and others area thoroughly reviewed.
• Radkevich, E. V. (2009), "Equations with nonnegative characteristic form. II", Journal of Mathematical Sciences, 158 (4): 453–604, doi:10.1007/s10958-009-9395-1, MR 2675371, S2CID 189871177, Zbl 1200.35157. This monograph consists of two volumes and is devoted to second-order partial differential equations (mainly, equations with nonnegative characteristic form). A number of problems of qualitative theory (for example, local smoothness and hypoellipticity) are presented, and the work of many contributors, like Olga Oleinik, Gaetano Fichera, the Author himself and others area thoroughly reviewed.

External links

• Kuperberg, Krystyna, ed. (2006), Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik – May 18–20, 2006, Berkeley, CA: AWM and MSRI, retrieved 1 July 2009. The proceedings of a workshop in honour of Olga Ladyzhenskaya and Olga Oleinik.
• O'Connor, John J.; Robertson, Edmund F., "Olga Oleinik", MacTutor History of Mathematics Archive, University of St Andrews.
• Olga Oleinik at the Mathematics Genealogy Project.
• Olga Oleinik at PlanetMath.
• Riddle, Larry, ed. (8 December 2010), Olga Arsen'enva Oleinik, retrieved 5 May 2011. A biography in the Biographies of Women Mathematicians, Agnes Scott College.