A. Molchanova

activity

20152026

most citedInjectivity almost everywhere and mappings with finite distortion in nonlinear elasticity

9 citations · 27 across the 12 of their papers we have counts for

collaborators

15 papers

math.AP2026

Derivation of variational membrane models in the context of anisotropic nonlocal hyperelasticity

Dominik Engl, Anastasia Molchanova, Hidde Schönberger

Motivated by the analysis of thin structures, we study the variational dimension reduction of hyperelastic energies involving nonlocal gradients to an effective membrane model. Whe…

math.AP2024

Linearization in magnetoelasticity

Stefano Almi, Martin Kružík, Anastasia Molchanova

Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangean one, we rigorously…

math.AP2023

A new example for the Lavrentiev phenomenon in Nonlinear Elasticity

Stefano Almi, Stefan Krömer, Anastasia Molchanova

We present a new example for the Lavrentiev phenomenon in context of nonlinear elasticity, caused by an interplay of the elastic energy's resistance to infinite compression and the…

math.FA2023

Differentiability almost everywhere of weak limits of bi-Sobolev homeomorphisms

Anna Doležalová, Anastasia Molchanova

This paper investigates the differentiability of weak limits of bi-Sobolev homeomorphisms. Given $p > n - 1$ , consider a sequence of homeomorphisms $f_{k}$ with positive Jacobians $J_{f_…

math.FA2022★ 4 cited

Weak limit of homeomorphisms in $W^{1, n - 1}$ : invertibility and lower semicontinuity of energy

Anna Doležalová, Stanislav Hencl, Anastasia Molchanova

Let $Ω$ , $Ω^{'} \subset R^{n}$ be bounded domains and let $f_{m} : Ω \to Ω^{'}$ be a sequence of homeomorphisms with positive Jacobians $J_{f_{m}} > 0$ a.e. and prescribed Dirichlet bou…

math.AP2021

Equilibria of charged hyperelastic solids

Elisa Davoli, Anastasia Molchanova, Ulisse Stefanelli

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by mea…

math.AP2020★ 4 cited

An extended variational theory for nonlinear evolution equations via modular spaces

Alexander Menovschikov, Anastasia Molchanova, Luca Scarpa

We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting…

math.FA2020

On grand Sobolev spaces and pointwise description of Banach function spaces

Pankaj Jain, Anastasia Molchanova, Monika Singh +1

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy…

math.CA2019

Injectivity almost everywhere for weak limits of Sobolev homeomorphisms

Ondřej Bouchala, Stanislav Hencl, Anastasia Molchanova

Let $Ω \subset R^{n}$ be an open set and let $f \in W^{1, p} (Ω, R^{n})$ be a weak (sequential) limit of Sobolev homeomorphisms. Then $f$ is injective almost everywhere for…

math.FA2019

A note on the continuity of minors in grand Lebesgue spaces

Anastasia Molchanova

We present a simple proof of the continuity, in the sense distributions, of the minors of the differential matrices of mappings belonging to grand Sobolev spaces. Such function spa…

math.FA2019

Regularity of the inverse mapping in Banach function spaces

Anastasia Molchanova, Tomáš Roskovec, Filip Soudský

We study the regularity properties of the inverse of a bilipschitz mapping $f$ belonging $W^{m} X_{loc}$ , where $X$ is an arbitrary Banach function space. Namely, we prove tha…

math.AP2018

A variational approximation scheme for elastodynamic problems using a new class of admissible mappings

Anastasia Molchanova

We consider a variational approximation scheme for the 3D elastodynamics problem. Our approach uses a new class of admissible mappings that are closed with respect to the space of…

math.FA2018★ 7 cited

Interpolation between H\" older and Lebesgue spaces with applications

Anastasia Molchanova, Tomáš Roskovec, Filip Soudský

Classical interpolation inequality of the type $∥ u ∥_{X} \leq C ∥ u ∥_{Y}^{θ} ∥ u ∥_{Z}^{1 - θ}$ is well known in the case when $X$ , $Y$ , $Z$ are Lebesgue spaces. In this paper we show t…

math.FA2017★ 9 cited

Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity

A. O. Molchanova, S. K. Vodop'yanov

We show that a sufficient condition for the weak limit of a sequence of $W_{q}^{1}$ -homeomorphisms with finite distortion to be almost everywhere injective for $q \geq n - 1$ , can be sta…

math.AP2015★ 3 cited

Variational problems of nonlinear elasticity theory in certain classes of mappings with finite distortion