Abstract
Sobolev homeomorphisms play a fundamental role in geometric function theory, calculus of variations, and continuum mechanics. In this talk, we discuss key properties of these mappings that are crucial from both modeling and analytical perspectives, such as continuity, injectivity, and Lusin's (N) and (N-1) conditions. We then present a variational model of elasticity, where the electroelastic energy incorporates the interaction between elastic response and electrostatics through a capacitary term defined in Eulerian coordinates. This results in an energy of mixed Lagrangian-Eulerian type. Finally, we analyze the continuity of these capacitary terms under deformation convergence and establish the existence of minimizers for the associated energy functional.
Brief Biography
Dr. Anastasia Molchanova defended her Ph.D. thesis in December 2016 at the Sobolev Institute of Mathematics in Russia. Since then, she has conducted research at the Sobolev Institute, Novosibirsk State University (Russia), the University of Vienna, and TU Wien (Austria). Currently, she holds a senior postdoctoral position at the Institute of Analysis and Scientific Computing at TU Wien, where she leads her own FWF Elise Richter project.
