Anastasia Molchanova

I am currently FWF Lise Meitner postdoc in the Reseach Group "Multiscale Calculus of Variations and PDEs", at the Institute of Analysis and Scientific Computing of TU Wien.

On March, 19th, 2020, I won the REWIRE grant (Maria Skłodowska-Curie Actions COFUND) with a project "Injectivity, Regularity, and Extensibility of Deformations". The project will be carried out at the University of Vienna in the near future.

Research

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My research is primarily concerned with quasiconformal and functional analysis, as well as analitical problems in materials science.
The aim of my research is to apply the methods of quasiconformal analysis to the various problems of nonlinear elasticity theory. In particular, the use of so-called mappings of finite distortion, rather than those traditionally used in such a context, should confer significant benefits since they directly encode much of the underlying physics.
Currently I am carrying out the Lise-Meitner project “Mappings of finite distortion for Nonlinear Solid Mechanics” (with Elisa Davoli as a co-applicant).
My research interests include:

quasiconformal analysis

Sobolev spaces

calculus of variations

geometric measure theory

function spaces

PDEs

Submitted publications

An extended variational theory for nonlinear evolution equations via modular spaces

preprint,

Selected publications

A. Molchanova, T. Roskovec, and F. Soudský, Regularity of the inverse mapping in Banach function spaces, To appear in Math. Nachr. 2020.
P. Jain, A. Molchanova, M. Singh, and S. Vodopyanov, On grand Sobolev spaces and pointwise description of Banach function spaces, Nonlinear Anal., 202 (2021).
O. Bouchala, S. Hencl, and A. Molchanova, Injectivity almost everywhere for weak limits of Sobolev homeomorphisms, J. Funct. Anal., 279:7 (2020).
A. O. Molchanova and S. K. Vodopyanov, Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity, Calc. Var. Partial Differential Equations, 59:17 (2020).
L. Kleprlík, A. O. Molchanova, and T. Roskovec, Example of a smooth homeomorphism violating the Lusin N⁻¹ condition, Sib. Math. J., 60:5 (2019), 886-895.
A. Molchanova, A note on continuity of minors in grand Lebesgue spaces, J. Fixed Point Theory Appl., 21:49 (2019).
F. Soudský, A. Molchanova, and T. Roskovec, Interpolation between Hölder and Lebesgue spaces, J. Math. Anal. Appl., 466:1 (2018), 160-168.
A. O. Molchanova, A variational approximation scheme for the elastodynamic problems in the new class of admissible mappings, Sib. J. Pure and Appl. Math., 16:3 (2016), 55–60 (Rus.).
S. K. Vodop'yanov and A. O. Molchanova, Lower semicontinuity of mappings with bounded (θ, 1)-weighted (p, q)-distortion, Sib. Math. J., 57:5 (2016), 778–787 (Rus.).

Dissertation thesis

A. Molchanova, Mappings with finite distortion and their applications in elasticity theory, Novosibirsk, 2016 (Rus.).

Conferences and meetings

Upcoming events

International Prague seminar on function spaces, December 17, 2020.
Winterschool on Analysis and Applied Mathematics, Münster, Germany, Februar 22-26, 2021.

Organized events

International conference on Geometric Analysis in honor of the 90th anniversary of academician Yu. G. Reshetnyak, Novosibirsk, Russia, September 22–28, 2019.
Youth Workshop on Analysis, Novosibirsk, Russia, June 27-29, 2018.
Mathematics in the Modern World, Novosibirsk, Russia, August 14-19, 2017.
Geometric Analysis and Control Theory, Novosibirsk, Russia, December 8-12, 2016.
School and Workshop on Dynamical systems, Geometry and Control Theory, Baikal Lake, Russia, July 6-17,2015.
Geometric Control Theory and Analysis on Metric Structure, Baikal Lake, Russia, August 3-8, 2014.
Geometric Control Theory and Analysis on Metric Structure, Teletskoe Lake, Gorno-Altaisk, Russia, July 25-30, 2014.
Multi-subject Workshop of Geometric Control Theory Laboratory of Sobolev Institute of Mathematics, Novosibirsk, Russia, December 16-27, 2013.

Teaching

2020 Winter semester, TU Wien, Introduction to space quasiconformal mappings

Contacts

Institute of Analysis and Scientific Computing TU Wien
Wiedner Hauptstraße 8-10, 1040 Wien, Austria
Office: DA 06 H22
anastasia.molchanova@tuwien.ac.at
+43 (1) 58801 10136