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39325-01 - Vorlesung: Calculus of Variations (8 KP)
| Semester | Frühjahrsemester 2017 |
| Weitere Semesterveranstaltungen zu diesen KP |
39325-01 (Vorlesung) 39325-02 (Übung) |
| Angebotsmuster | unregelmässig |
| Dozierende | Luca Martinazzi (luca.martinazzi@unibas.ch, BeurteilerIn) |
| Inhalt | The Calculus of Variations started in the second half of the XVII century in Basel with the Jakob Bernoulli, and developped with the fundamental works of Leonard Euler in Saint Petersburg and Joseph-Louis Lagrange in Turin. Since then it has flourished into a fundamental tool to describe and study the laws of physics (from classical mechanics, to relativity and quantum mechanics) and of geometric objects. We will start from its basic ideas and problems, moving towards the XIX problem of Hilbert about the regularity of minima of functionals in the calculus of variations and its solution given by Ennio De Giorgi. In between, we will address the elegant (and relatively simple) regularity theory for weak solutions of elliptic equations. The Calculus of Variation is one of the most active research fields in modern mathematics, hence this course is also suited for those who intend to continue their studies beyond the bachelor and master. |
| Literatur | M. Giaquinta, S. Hildebrandt, Calculus of Variations I, Springer M. Giaquinta, L. Martinazzi, An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs, 2nd edition, Edizioni della Normale. |
| Teilnahmevoraussetzungen | The partecipants should have taken the course "Reelle analysis" or something equivalent, where the integration in several variables (in the sense of Lebesgue) is discussed. |
| Unterrichtssprache | Englisch |
| Einsatz digitaler Medien | kein spezifischer Einsatz |
| HörerInnen willkommen |
| Intervall | Wochentag | Zeit | Raum |
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Keine Einzeltermine verfügbar, bitte informieren Sie sich direkt bei den Dozierenden.
| Module |
Vertiefungsmodul Analysis (Master Mathematik) |
| Prüfung | Lehrveranst.-begleitend |
| An-/Abmeldung zur Prüfung | Anm.: Belegen Lehrveranstaltung; Abm.: stornieren |
| Wiederholungsprüfung | keine Wiederholungsprüfung |
| Skala | Pass / Fail |
| Belegen bei Nichtbestehen | beliebig wiederholbar |
| Zuständige Fakultät | Philosophisch-Naturwissenschaftliche Fakultät, studiendekanat-philnat@unibas.ch |
| Anbietende Organisationseinheit | Fachbereich Mathematik |