Dušan Repovš

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

Education and academic career He graduated in 1977 from the University of Ljubljana. He obtained his PhD in 1983 from Florida State University with thesis Generalized Three-Manifolds with Zero-Dimensional Singular Set written under the direction of Robert Christopher Lacher. He held a fellowship from the Research Council of Slovenia and a Fulbright scholarship.

In 1993 he was promoted to Professor of Geometry and Topology at the University of Ljubljana, where he is employed at the Faculty of Mathematics and Physics and at the Faculty of Education, as the Head of the Chair for Geometry and Topology. Since 1983 he has been the leader of the Slovenian Nonlinear Analysis, Topology and Geometry Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana, the proof of the 4-dimensional Cellularity Criterion, and the proof of the Lipschitz case of the classical Hilbert–Smith conjecture. Presently he is most actively investigating in nonlinear analysis. Later he extended his research to several other areas and is currently most actively investigating problems of partial differential equations. He covers a very broad spectrum: problems with nonstandard growth (variable exponents, anisotropic problems, double-phase problems), qualitative analysis of solutions of semilinear and quasilinear PDEs (Dirichlet, Neumann, Robin boundary conditions), singular and degenerate problems (blow-up boundary, singular reactions), inequality problems (variational, hemivariational, both either stationary or evolutionary). His analysis of these problems combines fine methods at the interplay between nonlinear functional analysis, critical point theory, variational, topological and analytic methods, mathematical physics, and others.