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

    Prof. Dr. S. Müller erhält den diesjährigen Lehrpreis der Universität Bonn (07.07.17).

    Prof. Dr. Michael Ortiz kommt als Bonn Research Chair ans IAM (Pressemitteilung, 29.7.2016).

    Prof. Dr. S. Conti erhält den diesjährigen Lehrpreis der Universität Bonn (05.07.2016).

    Prof. Dr. Karl-Theodor Sturm, Koordinator des Hausdorff Zentrums für Mathematik an der Universität Bonn, erhält für seine eigene Forschung einen begehrten Advanced Grant des Europäischen Forschungsrats (ERC). (Pressemitteilung 21.04.2016)

    Prof. Dr. Stefan Müller has been invited to become full member of the scientific society “Academia Europaea” in November. Only European scientists, who have been recommended by a review board and are confirmed by a vote of the council, can join the society. (06.01.2016)

    Contact

    Managing Director: Prof. Dr. Anton Bovier
    Chief Administrator: Dr. B. Doerffel
    geschaeftsfuehrung@iam.uni-bonn.de
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    Mailing address

    Institute for Applied Mathematics
    University of Bonn
    Endenicher Allee 60
    D-53115 Bonn / Germany