Dušan Repovš

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Dušan D. Repovš

Dušan D. Repovš (born November 30, 1954 in Ljubljana ) is a Slovenian mathematician .

Life

Dušan Repovš graduated from the University of Ljubljana in 1977 and received his doctorate in 1983 from Florida State University with Robert Lacher (dissertation: Generalized Three-Manifolds with Zero-Dimensional Singular Set ). He had a grant from the Research Council of Slovenia and a Fulbright grant .

In 1993 he was promoted to Professor of Geometry and Topology at the University of Ljubljana , where he is head of the Department of Geometry and Topology at the Faculty of Mathematics and Physics and the Faculty of Education. Since 1983 he has been the head of the Slovenian Group for Nonlinear Analysis, Topology and Geometry at the Institute of Mathematics, Physics and Mechanics in Ljubljana and has headed numerous national and international research grants (with the United States, Japan, the Russian Federation, China, France, Italy, Spain, Israel, United Kingdom, Poland, Hungary, Romania, Slovakia and others). The Slovenian Research Agency selected this group as one of the best research program groups in Slovenia.

Repovš is the leading Slovenian expert in nonlinear analysis and topology and one of the most famous Slovenian mathematicians. He has published over 380 research papers and has given more than 400 invited lectures at various international conferences and universities around the world.

His research interests lie in topological methods in nonlinear analysis, applications of functional analysis, set-valued analysis, topology and algebra . He became known in the 1980s for his results in geometric topology, in particular the solution of the classical recognition problem for 3-manifolds , the proof of the 4-dimensional cellularity criterion and the proof of the Lipschitz case of the classical Hilbert-Smith conjecture about topological groups . He later expanded his research to several other areas and is currently researching partial differential equations . It covers a very broad spectrum: problems with non-standardized growth (variable exponents, anisotropic problems, double-phase problems), qualitative analysis of solutions to semilinear and quasilinear PDEs (Dirichlet, Neumann, Robin boundary conditions), singular and degenerate problems, inequality problems (variation, hemivariation, either stationary or evolutionary). His analysis of these problems combines sophisticated methods in the interplay of nonlinear functional analysis, theory of critical points, variations, topological and analytical methods, mathematical physics and others.

He is a member of the European Academy of Sciences and Arts , the New York Academy of Sciences , the American Mathematical Society , the European Mathematical Society , the London Mathematical Society , the Japanese Mathematical Society , the Moscow Mathematical Society and the French Mathematical Society , the Swiss Mathematical Society and Others. He is a founding member of the Slovenian Engineering Academy.

Awards

For his outstanding research he received an honorary doctorate from Craiova University in 2014 , the Bogolyubov Memorial Medal of the Ukrainian Mathematical Congress in Kiev in 2009 and the Prize of the Republic of Slovenia for Research in 1997 (today: Zois Prize). In 1995 he received the honorary title of Scientific Ambassador of the Republic of Slovenia for his promotion of Slovenian science abroad.

Fonts

  • NS Papageorgiou, VD Rǎdulescu, DD Repovš: Nonlinear Analysis - Theory and Methods, Springer Monographs in Mathematics, Springer, Cham 2019, MR3890060 .
  • D. Repovš: Asymptotics for singular solutions of the quasilinear logistic equation with absorption term, J. Math. Anal. Appl. 395: 1: 78-85 (2012) MR2943604 .
  • A. Cavicchioli, F. Hegenbarth, D. Repovš: Higher-Dimensional Generalized Manifolds: Surgery and Constructions, European Mathematical Society, Zurich 2016, MR3558558 .
  • VD Rădulescu, DD Repovš: Partial Differential Equations with Variable Exponents, Chapman and Hall / CRC 2015, MR3379920 .
  • A. Cavicchioli, D. Repovš, T. Thickstun: Geometric topology of generalized 3-manifolds, Journal of Mathematical Sciences, Volume 144, 2007, pp. 4413-4422, MR2192956 .
  • D. Repovš, PV Semenov: Continuous Selections of Multivalued Mappings, Kluwer Academic Publishers, Dordrecht 1998, MR1659914 .
  • Repovš: The recognition problem for topological manifolds: a survey, Kodai Math. J., Volume 17, 1994, pp. 538-548, MR1296925 , Project Euclid .

He serves on the editorial boards of the Journal of Mathematical Analysis and Applications, Advances in Nonlinear Analysis, Boundary Value Problems, Complex Variables and Elliptic Equations, and others.

Individual evidence

  1. ↑ Dušan Repovš in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ RJ Daverman, D. Repovš, General position properties that characterize 3-manifolds, Canad. J. Math. 44: 2, 234-251 (1992), MR 93d: 57038 .
  3. ↑ D. Repovš, A criterion for cellularity in a topological 4-manifold, Proc. Amer. Math. Soc. 100: 3: 564-566 (1987) MR891164 .
  4. ↑ D. Repovš, EV Ščepin, A proof of the Hilbert-Smith conjecture for actions by Lipschitz maps, Math. Ann. 1997 308: 2, 361-364, MR1464908 .
  5. ^ NS Papageorgiou, VD Radulescu and DD Repovš, Nonlinear Analysis - Theory and Methods, Springer, Cham 2019, MR3890060 .
  6. ↑ VD Radulescu, DD Repovš, Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis, Chapman and Hall / CRC, Taylor & Francis Group, Boca Raton, FL, 2015, MR3379920 .
  7. ^ Slovene Engineering Academy . Retrieved February 10, 2020.
personal data
SURNAME Repovš, Dušan
ALTERNATIVE NAMES Repovš, Dušan D.
BRIEF DESCRIPTION Slovenian mathematician and university professor
DATE OF BIRTH November 30, 1954
PLACE OF BIRTH Ljubljana