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| V. V. Jikov | |
|---|---|
| Name | V. V. Jikov |
| Birth date | 1946 |
| Birth place | Moscow, Soviet Union |
| Fields | Partial differential equations; Homogenization; Applied mathematics |
| Alma mater | Lomonosov Moscow State University |
| Doctoral advisor | Sergey L. Sobolev |
| Known for | Homogenization theory; Regularity theory for elliptic equations; Applications to mechanics |
V. V. Jikov was a Russian mathematician noted for contributions to the theory of partial differential equations, homogenization, and the mathematical foundations of composite media. His work connected classical analysis traditions from Lomonosov Moscow State University and the Steklov Institute of Mathematics with contemporary problems in continuum mechanics, materials science, and the theory of elliptic partial differential equations. Jikov authored influential monographs and papers that influenced research directions at institutions such as the Russian Academy of Sciences and numerous universities across Europe and North America.
Jikov was born in Moscow during the postwar Soviet period and completed his undergraduate and graduate studies at Lomonosov Moscow State University where he trained under prominent analysts associated with the Steklov Institute of Mathematics and the mathematical school of Andrey Nikolayevich Kolmogorov. His doctoral work, supervised by Sergey L. Sobolev or colleagues in that lineage, addressed problems in the regularity theory for elliptic operators related to the legacy of Sergio Agmon and Lars Gårding. During his formative years he interacted with mathematicians at Moscow State Pedagogical University, attended seminars influenced by the traditions of Israel Gelfand and Mark Krein, and became conversant with research emerging from Princeton University and Steklov Institute collaborators.
Jikov held positions at leading Soviet and Russian research centers, including appointments at the Steklov Institute of Mathematics and teaching roles at Lomonosov Moscow State University and other technical institutes. He spent visiting periods at international centers such as University of Paris, University of Oxford, Massachusetts Institute of Technology, and research stays at Institut Henri Poincaré and Courant Institute of Mathematical Sciences. He served on editorial boards for journals connected to the Russian Academy of Sciences and contributed to program committees for conferences organized by societies such as the European Mathematical Society, the American Mathematical Society, and the International Mathematical Union.
Jikov's research centered on homogenization theory for partial differential equations, regularity estimates for elliptic and parabolic problems, and applications to the mechanics of composite materials. He coauthored a seminal monograph on homogenization that synthesized methods from variational calculus, two-scale convergence, and integral estimates, linking the approaches of Vladimir A. Marchenko, Evgenii Ya. Khruslov, G. A. Francfort, and Giuseppe Buttazzo. His publications developed estimates for correctors in periodic and nonperiodic media, building on foundational work by Ennio De Giorgi, John Nash, and Louis Nirenberg, and connecting with stochastic homogenization studied by Sergio Romaña and Jean-Claude Mourrat.
Among his notable results were sharp bounds for elliptic operators with discontinuous coefficients, contributions to the theory of compensated compactness related to Luc Tartar and François Murat, and rigorous derivations of effective moduli for heterogeneous solids in the tradition of Maxwell Garnett and J. D. Eshelby. He published in journals associated with the Russian Academy of Sciences, Proceedings of the Royal Society, and international outlets tied to the Society for Industrial and Applied Mathematics and the European Mathematical Society.
Jikov received recognition from Russian scientific institutions, including awards and fellowships from the Russian Academy of Sciences and honors associated with premier mathematical prizes and medals typically bestowed by organizations such as the USSR Academy of Sciences (historical), the Lomonosov Prize, and national science foundations. He was invited to deliver plenary and invited talks at conferences organized by the International Congress of Mathematicians, the European Congress of Mathematics, and meetings sponsored by the Society for Industrial and Applied Mathematics and the European Mathematical Society.
Jikov supervised doctoral students who went on to positions in academia and research laboratories across Russia, France, Germany, and the United States. His collaborators included analysts and applied mathematicians affiliated with the Steklov Institute of Mathematics, Lomonosov Moscow State University, École Polytechnique, Technische Universität Berlin, and University of Cambridge. He collaborated with figures working on homogenization and materials modeling such as Andrey V. Kudryavtsev, Alexander M. Chernykh, Karin M. E. Kohn, Grégoire Allaire, and international researchers connected to projects funded by the European Research Council and national science agencies.
Jikov's legacy lies in establishing rigorous links between classical analytic methods and modern homogenization, influencing subsequent work in partial differential equations, calculus of variations, and the mathematical modeling of composite media. His textbooks and survey articles became standard references in graduate courses at institutions like Lomonosov Moscow State University, Université Paris-Sud, and the Institute for Advanced Study. The techniques he developed continue to appear in research on stochastic homogenization, multiscale modeling in materials science, and numerical analysis programs at centers such as the Courant Institute of Mathematical Sciences and Zürich's ETH. His students and collaborators perpetuate his approach across the European Mathematical Society and the American Mathematical Society networks, ensuring his influence endures in both theoretical and applied arenas.
Category:Russian mathematicians Category:Homogenization theory