Contact information

Address: Institutt for matematiske fag
NTNU
Alfred Getz' vei 1
N-7491, Trondheim
Norway
E-mail: sigmund.selberg@math.ntnu.no
Telephone: (+47) 73 55 02 84 (Office)
(+47) 400 43 660 (Mobile)
Telefax: (+47) 73 59 35 24

Teaching
2009 Høst: TMA4100 Matematikk 1
Vår TMA4105 Matematikk 2
2007 Vår TMA4305 Partielle diff.lign.
2006 Høst: TMA4100 Matematikk 1
Vår: TMA4305 Partielle diff.lign.
2005 Høst: TMA4130 Matematikk 4N
Vår: TMA4105 Matematikk 2
2004 Høst: TMA4130 Matematikk 4N
Vår: TMA4105 Matematikk 2
2003 Høst: TMA4130 Matematikk 4N

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Research

Papers in preparation:

  1. A combinatorial calculus for quadrilinear forms associated to the wave equation. In preparation.

Submitted:

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Accepted, awaiting publication:

  1. Finite-energy global well-posedness of the Maxwell-Klein-Gordon equations in Lorenz gauge. (With A. Tesfahun.) To appear in Communications in PDE
  2. On the Maxwell-Klein-Gordon equations in Lorenz gauge. (With A. Tesfahun.) To appear in the proceedings of the International Congress of Mathematical Physics 2009
  3. Product estimates for wave-Sobolev spaces in 1+1 and 1+2 dimensions. (With P. D'Ancona and D. Foschi.) To appear in a special volume based on a one-year program in Nonlinear PDEs at the Centre for Advanced Study (CAS) at the Norwegian Academy of Sciences
  4. Atlas of products for wave-Sobolev spaces on R1+3. (With P. D'Ancona and D. Foschi.)
    5. To appear in Transactions of the AMS.
  5. Null structure and almost optimal local well-posedness of the Maxwell-Dirac system. (With P. D'Ancona and D. Foschi.) To appear in Amer. J. Math.
  6. Low regularity well-posedness for some nonlinear Dirac equations in one space dimension. (With A. Tesfahun.) To appear in Differential and Integral Equations
  7. Remarks on regularity and uniqueness of the Dirac-Klein-Gordon equations in 1d. (With A. Tesfahun.) To appear in Nonlinear Differential Equations and Applications (NoDEA).

Published:

  1. Low regularity solutions of the Maxwell-Dirac system. (With P. D'Ancona and D. Foschi.) Hyperbolic Problems (HYP2008): Theory, Numerics and Applications. Plenary and Invited Talks. AMS Proceedings of Symposia in Applied Mathematics (2009). Pages 243-252
  2. Anisotropic bilinear L2 estimates related to the 3D wave equation. IMRN (2008). pdf.
  3. Low regularity well-posedness of the Dirac-Klein-Gordon system in one space dimension. With A. Tesfahun. Commun. Contemp. Math. 10 (2008) no. 2, 181-194. pdf.
  4. Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system. (With P. D'Ancona and D. Foschi.) Journal of the EMS 9 (2007) no. 4, 877-898. pdf.
  5. Global well-posedness below the charge norm for the Dirac-Klein-Gordon system in one space dimension. IMRN (2007). pdf.
  6. Local well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions. (With P. D'Ancona and D. Foschi.) Journal of Hyperbolic Differential Equations (2007), no. 2, 295-330. pdf.
  7. Convergence of the Dirac-Maxwell system to the Vlasov-Poisson system. (With N. J. Mauser.) Communications in PDE 32 no. 3, (2007), 503-524. pdf.
  8. On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit. (With P. Bechouche and N. J. Mauser.) Journal of Hyperbolic Differential Equations 2 (2005), no. 1, 129-182. pdf.
  9. Nonrelativistic limit of Klein-Gordon-Maxwell to Schrödinger-Poisson. (With P. Bechouche and N. J. Mauser.) American Journal of Mathematics 126 (2004), no. 1, 31-64. pdf.
  10. Derivation of Schrödinger-Poisson as the non-relativistic limit of Klein-Gordon Maxwell. (With P. Bechouche and N. J. Mauser.) Hyperbolic problems: theory, numerics, applications, 357--367, Springer, Berlin, 2003.
  11. Almost optimal local well-posedness of the Klein-Gordon-Maxwell system in 1+4 dimensions. Communications in PDE 27 (2002), 1183-1227. pdf
  12. Bilinear estimates and applications to nonlinear wave equations. (With Sergiu Klainerman.) Commun. Contemp. Math. 4 (2002), 223-295. pdf
  13. On an estimate for the wave equation and applications to nonlinear problems. Differential and Integral Equations 2 (2002), 213-236. pdf
  14. Remark on the optimal regularity for equations of wave maps type. (With Sergiu Klainerman.) Communications in PDE 22 (1997), 901-918. pdf

Thesis:

Multilinear spacetime estimates and applications to local existence theory for nonlinear wave equations. Ph.D. Thesis, Princeton University 1999. pdf. Advisor: Sergiu Klainerman.

Lecture notes:

In the spring semester 2001 I gave a graduate course on nonlinear wave equations at Johns Hopkins University. The course notes can be downloaded here: pdf.

Slides:

Here is a presentation from a talk I gave in the DIFTA seminar at NTNU: DIFTAtalk06.pdf

Links

 MathSciNet

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Sigmund Selberg :: Institutt for matematiske fag :: NTNU