Universität Wien FIND

250136 VU Lower semicontinuity of integral functionals and applications (2021W)

2.00 ECTS (1.00 SWS), SPL 25 - Mathematik
Prüfungsimmanente Lehrveranstaltung


Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").


max. 20 Teilnehmer*innen
Sprache: Englisch



First unit: 10.1.2021 9 - 12 UhrFurther unit: 12.1., 14.1., 17.1., jeweils 9 - 12 UhrLast unit: 19.1.2021 9 - 11 UhrLocation: Erwin Schrödinger Institut für Mathematik und Physik,Boltzmanngasse 9, 1090 Wien Erwin Schrödinger Hörsaal


Ziele, Inhalte und Methode der Lehrveranstaltung

In 1830, B. Bolzano observed that continuous functions attain extreme values on compact intervals of reals. This idea was then significantly extended around 1900 by D. Hilbert who set up a framework, called the direct method, in which we can prove existence of minimizers/maximizers of nonlinear functionals. Semicontinuity plays a crucial role in these considerations. In 1965, N.G. Meyers significantly extended lower semicontinuity results for integral functionals depending on maps and their gradients available at that time. We recapitulate the development
on this topic from that time on. Special attention will be paid to applications in continuum mechanics of solids. In particular, we review existing results applicable in nonlinear elasticity and emphasize the key importance of convexity and subdeterminants of matrix-valued gradients. Finally, we mention a couple of open problems and outline various generalizations of these results to more general first-order partial differential operators with applications to electromagnetism, for instance.

Art der Leistungskontrolle und erlaubte Hilfsmittel

oral exam

Mindestanforderungen und Beurteilungsmaßstab

Acquaintance with the fundamental concepts discussed in the
course, as well as the related proof strategies.


Discussion on the topics of the course and/or short
presentation on assigned materials


Zuordnung im Vorlesungsverzeichnis


Letzte Änderung: Mi 29.09.2021 10:49