Institute for applied mathematics

Applied Analysis - Teaching

Summer Term 2015


V5B2 - Selected Topics in Analysis and PDE

 

IMPORTANT: Additional lecture on 29th June 12-14, SR 0.008!

 

Lecturer: Flaviana Iurlano

 

Location: Wednesday 12-14, room MATH / SemR 0.011

 

Period: April 8 - July 15

 

Description:

 

Part I: BV-functions

  • Vector valued Radon measures and weak convergence
  • Definition and properties of BV (semicontinuity of the total variation, embedding theorems, approximation by smooth functions, trace on the boundary)
  • Sets with finite perimeter and Hausdorff measure
  • Coarea formula
  • Fine properties of BV-functions and structure of the gradient
  • Slicing
  • The space SBV, compactness and lower semicontinuity theorem in SBV

Part II: Applications

  • Gradient theory of phase transitions
  • Approximation of the Mumford-Shah functional for image segmentation
  • Convergence of damage models to fracture models

References:

  1. L. Ambrosio, N. Fusco, D. Pallara, Functions of bounded variations and free discontinuity problems, Oxford University Press
  2. L.C. Evans, R.F. Gariepy, Measure theory and fine properties of functions, CRC Press
  3. E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser Verlag
  4. L. Modica, The gradient theory of phase transitions and the minimal interface criterion, ARMA (1987)
  5. L. Modica, S. Mortola, Un esempio di Γ-convergenza, BUMI (1977)
  6. L. Ambrosio, V.M. Tortorelli, On the approximation of free discontinuity problems, BUMI (1992)
  7. S. Conti, M. Focardi, F. Iurlano, Phase field approximation of cohesive fracture models, AIHP (2015)

Oral examination:   20/07/2015 and 21/09/2015. Please send an email to iurlano(at)iam.uni-bonn.de to register.

 

 

 

 

    News

    Die ehemalige Doktorandin am IAM, Lisa Hartung (aktuell: Courant Institute of Mathematical Sciences, New York), wurde für ihre herausragende Doktorarbeit "Extremal Processes in Branching Brownian Motion and Friends" (Betreuer: Prof. Bovier) mit dem Förderpreis der DMV-Fachgruppe Stochastik ausgezeichnet. Details hier. (14.03.2018)

    Prof.  Patrik Ferrari erhält den ersten Alexandros Award zusammen mit Ivan Corwin (Columbia University) und Alexei Borodin (MIT) für den Artikel "Free energy fluctuations for directed polymers in random media in 1+1 dimensions".
    Details siehe hier. (12.03.2018)

    Frau Dr. Martina Vera Baar erhält den Hausdorff-Gedächtnispreis für die beste Dissertation des akademischen Jahres 2016/17 (Betreuer: Prof. Dr. A. Bovier, IAM). (Pressemitteilung, 24.01.2018)

    Contact

    Managing Director: Prof. Dr. Anton Bovier
    Chief Administrator: Dr. B. Doerffel
    geschaeftsfuehrung@iam.uni-bonn.de
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    Institute for Applied Mathematics
    University of Bonn
    Endenicher Allee 60
    D-53115 Bonn / Germany