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Nonlinear Analysis (2005)

Organizers: Henrik Shahgholian (Stockholm), Peter Markowich (WPI c/o Univ. Vienna)

  • (Co-funded with ESF program Global)

    • This Thematic Program aims at the study of properties of solutions of nonlinear partial differential equations (PDE) and free boundary problems (FBP) from the viewpoints of theory and applications.

    The investigation of global and geometric properties of solutions of partial differential equations is a key research area in mathematics that has many practical applications. The focus of this program will be on problems where not only geometric aspects will play a central role but also the fact that a-priori the domain under consideration is unknown (whence the name FBP).

    Regularity questions of unknown sets have been in focus for several decades. Many times, modeling phenomena in nature by partial differential equations give rise to unknown boundaries. It is of great importance to analyze these boundaries from a rigorous mathematical point of view. Recent years have also seen many new directions as well as new techniques entering into this very technical field. Several areas such as potential theory, micromagnetics, image processing, computer vision, geometric measure theory, free boundary problems in physics/mechanics, and many other subjects have gained or regained from the new techniques.

    The local study of solutions of PDEs is often carried out through a "zooming" technique or blow-up analysis. This procedure reduces the problem to the classification of global solutions (solutions in the whole space). It is often employed, for instance, for minimal surfaces, free boundary problems and for semilinear equations.

    Similar global symmetry questions are now under study in relation with problems where the reaction only takes place on the boundary, and in the interior of the material there is only diffusion. Phase transition type (or layer) solutions are for first time under analysis. Here, as in the famous (and partially solved) conjecture of De Giorgi, the combination of PDE and variational tools provides very strong techniques.

    A further theme in focus is the theory of optimal stopping, central in economics. For example,

    1. the problem of finding the optimal time of starting (or stopping) an economic activity under uncertainty can often be formulated as an optimal stopping problem.
    2. Second, it has been proved that the price of an American option in finance is given by the solution of an optimal stopping problem. Today it is well known that an optimal stopping problem for a diffusion is equivalent to a free boundary problem, and such problems are again equivalent to certain variational inequalities involving partial differential operators (the generators of the underlying diffusions). We need to solve the corresponding PDEs in the so-called continuation region and combine this with high contact (smoothness) conditions. This gives an explicit link between PDEs and optimal stopping and hence with finance.

      3. Events

      Workshop on Free Boundaries and PDEs in Biology

      Location: WPI Nordbergstr. 15 /
      Time: 21. Mar 2006 (Tue) - 22. Mar 2006 (Wed); Opening: 9:00
      Organiser(s)
      Danielle Hilhorst (Univ. Paris sud)
      Christian Schmeiser (WPI and Univ. of Vienna)
      Henrik Shagholian (KTH Stockholm)
      Remark: Program

      Workshop "Symmetries of solutions of nonlinear elliptic PDEs

      Location: Nordbergstrasse 15/
      Time: 23. Jan 2006 (Mon) - 27. Jan 2006 (Fri); Opening: 10:00
      Organiser(s)
      Henrik Shahgholian (henriksh@kth.se)
      Wolfgang Reichel (wolfgang.reichel@math.unizh.ch)
      Alberto Farina (alberto.farina@u-picardie.fr)

      New developments in Hele-Shaw flow (or Laplacian growth)

      Location: WPI Nordbergstraße, Seminar Room
      Time: 13. Dec 2005 (Tue) - 13. Dec 2005 (Tue); Opening: 9:00
      Organiser(s)
      Björn Gustafsson (KTH Stockholm)
      Henrik Shahgholian (KTH Stockholm)

      Conference on nonlinear PDEs in honor of Luis Caffarelli

      Location: Nordbergstraße 15, UZA 4, Rooms 206 and 207
      Time: 24. Oct 2005 (Mon) - 25. Oct 2005 (Tue); Opening: 9:00
      Organisation(s)
      WPI
      CNRS       		Organiser(s)
      Alberto Farina (Inst. CNRS Pauli)
      Peter Markowich (WPI c/o Univ. Wien)
      Contact: wittgenstein.mathematik@univie.ac.at
      Remark: Confirmed speakers: L. Caffarelli, I. Gamba, T. Souganidis, H. Shahgholian, J.L.Vazquez, A.Farina
      Program

      NLPDE 05 : Summer School and Workshop on "Non Linear PDEs" (external website )

      Location: Seminar Room C207, Fak.f. Mathematik, Nordbergstr. 15, UZA4
      Time: 19. Jul 2005 (Tue) - 27. Jul 2005 (Wed); Opening: 14:00
      Topics:
      Joint event of the EU network HYKE with the WPI Programm on Nonlinear PDEs and Applications and the ESF programme on "Global and Geometric Aspects of Nonlinear PDEs" of H. Shahgholian and P. Markowich . A 4 days school will be followed by a 3 days workshop
      Organisation(s)
      WPI       		Organiser(s)
      Yann Brenier , CNRS Nice
      Peter Markowich , WPI c/o Vienna University
      Norbert J. Mauser , WPI c/o Vienna University
      Henrik Shahgholian , Royal Institute of Technology (KTH), Stockholm

      Workshop "PDEs in Industry and Engineering" (external website )

      Location: Vienna/Strobl
      Time: 26. Jun 2005 (Sun) - 30. Jun 2005 (Thu); Opening: 14:00
      Topics:
      "Semiconductor modeling using quantum mechanical, kinetic and fluid dynamical models" "Free boundary problems in flame propagation" "Semiclassical analysis of Schroedinger equations with applications to quantum mechanical systems, eg Bose-Einstein condensation"
      Organisation(s)
      WPI
      ALFA Project "PDEs in Industry and Engineering
      Wittgenstein Award - Peter Markowich       		Organiser(s)
      Peter A. Markowich , University of Vienna, WPI
      Jorge P. Zubelli , IMPA, Rio de Janeiro, Brazil
      Remark: Contact/Information: Renate Feikes, wittgenstein.mathematik@univie.ac.at

      Talks in the framework of this thematic program... (by date) , (by name)

      Pauli Fellows

      Shahgholian, Henrik 1. Apr 2005-31. Mar 2006 local address 

      Visitors

      Achleitner, Franz 19. Jul 2005-27. Jul 2005 local address 
      Aoki, Kazuo 30. May 2005-1. Jun 2005 local address 
      Apushkinskaya, Darya 20. Apr 2005-22. Apr 2005 local address 
      22. Nov 2005-24. Nov 2005 local address 
      Athanasopoulos, Joannis 25. May 2005-28. May 2005 local address 
      23. Oct 2005-26. Oct 2005 local address 
      Bandle, Catherine 13. Mar 2005-15. Mar 2005 local address 
      22. Jan 2006-27. Jan 2006 local address 
      Bardos, Claude 20. Jul 2005-29. Jul 2005 local address 
      Bozorgnia, Farid 16. Jul 2005-2. Aug 2005 local address 
      Brenier, Yann 18. Jul 2005-28. Jul 2005 local address 
      Brock, Friedemann 22. Jan 2006-27. Jan 2006 local address 
      Bucur, Dorin 19. Apr 2005-22. Apr 2005 local address 
      Caffarelli, Luis 23. Oct 2005-25. Oct 2005 local address 
      Calahorranno, Marco 13. Sep 2005-27. Sep 2005 local address 
      Corrado, Lattanzio 20. Jun 2005-23. Jun 2005 local address 
      Damascelli, Lucio 21. Jan 2006-25. Jan 2006 local address 
      Dhamo, Elidon 18. Jul 2005-27. Jul 2005 local address 
      Edquist, Anders 16. Jul 2005-2. Aug 2005 local address 
      Farina, Alberto 1. Aug 2005-31. Jul 2006 local address 
      Firt, Roman 19. Jul 2005-24. Jul 2005 local address 
      Gamba, Irene 23. Oct 2005-25. Oct 2005 local address 
      Gottlieb, Dr., Alexander 1. Jul 2005-30. Jul 2005 local address 
      Gualdani, Maria Pia 19. Jul 2005-27. Jul 2005 local address 
      Gustafsson, Björn 11. Dec 2005-14. Dec 2005 local address 
      Ha, Seung Yeal Nonlinear Analsysis 3. Jan 2006-24. Jan 2006 local address 
      Hainzl, Christian 1. Jul 2005-7. Jul 2005 local address 
      Haskovec, Jan 19. Jul 2005-27. Jul 2005 local address 
      Hedenmalm, Hakan 12. Dec 2005-16. Dec 2005 local address 
      Henrot, Antoine 24. Jan 2006-26. Jan 2006 local address 
      Holden, Helge 22. Jul 2005-24. Jul 2005 local address 
      Huang, Zhongyi Nonlinear Analysis , Visitor 1. Feb 2006-16. Feb 2006 local address 
      Kamotski, Vladimir 18. Jul 2005-29. Jul 2005 local address 
      Kawohl, Bernd 22. Jan 2006-27. Jan 2006 local address 
      Klein, Christian 14. Jun 2005-16. Jun 2005 local address 
      Lee, Ki-ahm 25. May 2005-28. May 2005 local address 
      Lindgren, Erik 16. Jul 2005-2. Aug 2005 local address 
      Lörincszi, Jozsef (Senior Researcher) 15. Jun 2005-17. Jun 2005 local address 
      Lucia, Marcello 23. Jan 2006-27. Jan 2006 local address 
      Manfredi, Juan 19. Jul 2005-23. Jul 2005 local address 
      McKenna, Joe 24. Jan 2006-29. Jan 2006 local address 
      Milakis, Emanouil 18. Jul 2005-27. Jul 2005 local address 
      Natalini, Roberto 22. Jul 2005-24. Jul 2005 local address 
      Nyström, Kaj 22. Jan 2006-27. Jan 2006 local address 
      Pacella, Filomena 23. Jan 2006-29. Jan 2006 local address 
      Pallard, Christophe 18. Jul 2005-23. Jul 2005 local address 
      Rascle, Michel 19. Jul 2005-28. Jul 2005 local address 
      Reichel, Wolfgang 23. Jan 2006-27. Jan 2006 local address 
      Roselli, Paolo 23. Jan 2006-27. Jan 2006 local address 
      Sciunzi, Berardino 23. Jan 2006-27. Jan 2006 local address 
      Selberg, Sigmund 24. Jul 2005-28. Jul 2005 local address 
      Shahgholian, Henrik 23. Oct 2005-25. Oct 2005 local address 
      22. Nov 2005-24. Nov 2005 local address 
      Shashahani, Mehrdad Nonlinear Analysis (2005) 23. Oct 2005-28. Oct 2005 local address 
      Sirakov, Boyan 20. Jan 2006-26. Jan 2006 local address 
      Sirito, Gabriele 19. Jul 2005-27. Jul 2005 local address 
      Slateff, Andreas 19. Jul 2005-27. Jul 2005 local address 
      Souganidis, Takis 23. Oct 2005-25. Oct 2005 local address 
      Trabelsi, Saber 17. Jul 2005-31. Jul 2005 local address 
      Uraltseva, Nina 22. Nov 2005-24. Nov 2005 local address 
      Vasiliev, Alexander 10. Dec 2005-14. Dec 2005 local address 
      Vasseur, Alex 19. Jul 2005-28. Jul 2005 local address 
      Vazquez, Juan Luis 13. Mar 2005-15. Mar 2005 local address 
      23. Oct 2005-25. Oct 2005 local address 
      Westdickenberg, Michael 19. Jul 2005-27. Jul 2005 local address 
      Weth, Tobias 22. Jan 2006-28. Jan 2006 local address 
      Willem, Michel 22. Jan 2006-27. Jan 2006 local address 
      Wolanski, Noemi 25. May 2005-29. May 2005 local address 

      PostDocs

      DiFrancesco, Marco 1. Nov 2005-31. Mar 2006 local address 
      Komech, Alexander 1. Jul 2005-31. Dec 2006 local address 
      Pallard, Christophe 1. Oct 2005-31. Dec 2005 local address 

      PreDocs

      Tarquini, Emilien 4. Jan 2006-28. Jan 2006 local address 
    Impressum webmaster [Printable version]