mathematics

Olga Oleinik

Olga Oleinik is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Olga Oleinik rather than just read about it. In short: 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.

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Reference excerpt

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. 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.

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 a 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.), Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990), 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

References

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Illustrations

Worked examples

Example 1 — a first encounter with Olga Oleinik

Start with the simplest possible case. Write down what Olga Oleinik claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Olga Oleinik before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Olga Oleinik ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Olga Oleinik

In research: Olga Oleinik appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Olga Oleinik in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Olga Oleinik is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2001 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Olga Oleinik outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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