RNDr. Luděk Kleprlík, Ph.D.


Selected topics in non-linear functional analysis and approximation theory

Junior Grants
Czech Science Foundation
2018 - 2021
Non-linear functional analysis deals with problems concerning mappings of various regularity between Banach spaces and their subsets. In particular, it studies the characterization of Banach spaces by their metric structure and the stability of certain properties under non-linear homeomorphisms or embeddings. One of very important tools is so-called Lipschitz-free Banach spaces, the preduals of spaces of Lipschitz functions, which provide an abstract linearization of Lipschitz maps between metric spaces. In our research, we plan to study some open questions concerning the structure (universality, embeddings, weak sequential completeness, complementability) and approximation properties of Lipschitz-free spaces. Next, we plan to address the question whether a Sobolev homeomorphism can be approximated by diffeomorphisms or piecewise affine homeomorphisms, which is a problem of great significance in non-linear elasticity theory, PDE's and calculus of variations.