Anastasia Molchanova

I am currently an Elise Richter fellow at the Institute of Analysis and Scientific Computing at TU Wien with my project “Global and Local Behavior of Deformations”.

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My research is primarily concerned with analysis — especially functional and quasiconformal analysis, as well as with calculus of variations and its application in materials science. I am also interested in geometric measure theory, control theory, sub-Riemannian geometry, and PDEs. After completing my Ph.D.-thesis on quasiconformal analysis, I am carrying out my research at the interface between these fields and binding them up together.
Besides research, I am a member of the Austrian Association of Women in Mathematics (A²WiM).

You can meet me at
Fractional Sobolev Spaces, TU Wien, WS2024 Thursdays 8:30-11:30;
Vienna Geometric Analysis Seminar, University of Vienna, second Wednesday of every month at 11:30-13:00;
Infinite-dimensional Geometry: Theory and Applications, ESI, Vienna, January 13 - February 14, 2025.

Publications

Download a full list of publications as pdf or bib

S. Almi, M. Kružik, and A. Molchanova, Linearization in Magnetoelasticity, Preprint arXiv, 2024.
A. Doležalová, S. Hencl, and A. Molchanova, Weak limit of homeomorphisms in W^1,n−1: invertibility and lower semicontinuity of energy, ESAIM: Control, Optimisation and Calculus of Variations, 30 (2024), 37.
A. Doležalová and A. Molchanova, Differentiability almost everywhere of weak limits of bi-Sobolev homeomorphisms, Pure and Applied Functional Analysis, 9:2 (2024), 427–440; arXiv.
S. Almi, S. Krömer, and A. Molchanova. A new example for the Lavrentiev phenomenon in Nonlinear Elasticity, Zeitschrift für Angewandte Mathematik und Physik, 75, 2 (2024).
S. K. Vodopyanov, A. O. Molchanova. The boundary behavior of Q_q,p-homeomorphisms, Izvestiya: Mathematics 87:4 (2023), 683-725.
E. Davoli, A. Molchanova, and U. Stefanelli, Equilibria of charged hyperelastic solids, SIAM J. Math. Anal. (SIMA) 54:2 (2022), 1470-1487.
A. Molchanova, T. Roskovec, and F. Soudský, Regularity of the inverse mapping in Banach function spaces, Math. Nachr. 294:12 (2021), 2382-2395.
A. Menovschikov, A. Molchanova, L. Scarpa, An extended variational theory for nonlinear evolution equations via modular spaces, SIAM J. Math. Anal. (SIMA), 53:4 (2021), 4865-4907.
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.
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.).

Third-party funds

FWF Elise Richter grant with a project “Global and Local Behavior of Deformations”, 404K €, 4 years, 2023-2027.
Grant for the organization of the ESI (Erwin Schrödinger Institute) Workshop "Between Regularity and Defects: Variational and Geometrical Methods in Materials Science" (organizers: Stefano Almi and Anastasia Molchanova), 16K €, February 20-24, 2023.
REWIRE grant (Maria Skłodowska-Curie Actions COFUND) with a project "Injectivity, Regularity, and Extensibility of Deformations" (mentor: Ulisse Stefanelli), 266K €, 3 years, 2021-2024.
FWF Lise Meitner grant with a project “Mappings of finite distortion for Nonlinear Solid Mechanics” (mentor: Elisa Davoli), 159K €, 2 years, 2019-2021.

Teaching

2024 Winter Semester, TU Wien, advanced lecture course Fractional Sobolev Spaces
2022 Summer Semester, UniVie, lectures with integrated exercises on Analysis for Computational Science
09/2021, Mini-course on Variational capacity and how to use it, The First Conference of Young Applied Mathematicians in Leuca, Italy
02/2021, Mini-course on Introduction to Γ-convergence, Faculty of Mechanics and Mathematics, Novosibirsk State University, Russia
2021 Winter Semester, UniVie, tutorials on Advanced Analysis and Differential Geometry
2020 Winter Semester, TU Wien, advanced lecture course Introduction to space quasiconformal mappings
2018 Summer Semester, Novosibirsk State University, Quasiconformal mappings in Nonlinear Elasticity within the advanced lecture course Introduction to Geometric Analysis
2013-2018, Novosibirsk State University, tutorials on Mathematical Analysis

Contacts

Institute of Analysis and Scientific Computing, TU Wien.
Wiedner Hauptstraße 8-10, 1040 Wien - Office DA 04 E22
anastasia.molchanovatuwien.ac.at
+43 (1) 58801 10130