Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Analysis-Seminar Augsburg-München


Professor Dr. Carolin Kreisbeck
Katholische Universität Eichstätt-Ingolstadt

spricht am
Donnerstag, 15. Juni 2023
16:30 Uhr
Raum 2004 (L1)
über das Thema:

»A variational theory for integral functionals involving finite-horizon fractional gradients«

Motivated by new nonlocal models in hyperelasticity, we discuss a class of variational problems with integral functionals depending on nonlocal gradients that correspond to truncated versions of the Riesz fractional gradient. We address several aspects regarding the existence theory of these problems and their asymptotic behavior. Our analysis relies on suitable translation operators that allow us to switch between the three types of gradients: classical, fractional, and nonlocal. These provide helpful technical tools for transferring results from one setting to the other. Based on this approach, we show that quasiconvexity, the natural convexity notion in the classical calculus of variations, characterizes the weak lower semicontinuity also in the fractional and nonlocal setting. As a consequence of a general Gamma-convergence statement, we derive relaxation and homogenization results. The analysis of the limiting behavior as the fractional order tends to 1 yields localization to a classical model. This is joint work with Javier Cueto (University of Nebraska-Lincoln) and Hidde Schönberger (KU Eichstätt-Ingolstadt).


Hierzu ergeht herzliche Einladung.
Prof. Dr. Dirk Blömker

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).

[Impressum]      [Datenschutz],     Mo 22-Mai-2023 09:12:46 MESZ