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

2011 Høst: TMA4100 Matematikk 1
2010 Høst: TMA4100 Matematikk 1
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

Submitted:

  1. Null structure and local well-posedness in the energy class for the Yang-Mills equations in Lorenz gauge. (With A. Tesfahun.)

Published:

  1. Global well-posedness of the Chern-Simons-Higgs equations with finite energy. (With A. Tesfahun.) Discrete and Continuous Dynamical Systems. Volume 33, Number 6, June 2013
  2. Unconditional uniqueness in the charge class for the Dirac-Klein-Gordon equations in two space dimensions. (With A. Tesfahun.) Nonlinear Differential Equations and Applications (NoDEA). 20 (2013), 1055-1063
  3. Dispersive estimate for the 1D Schrödinger equation with a steplike potential. (With P. D'Ancona.) Journal of Differential Equations. 252 (2012) 1603-1634
  4. Atlas of products for wave-Sobolev spaces on R1+3. (With P. D'Ancona and D. Foschi.) Transactions of the AMS. 364 (2012), 31-63
  5. Bilinear Fourier restriction estimates related to the 2d wave equation. Advances in Differential Equations Volume 16, Numbers 7-8, 2011, Pages 667-690
  6. Global well-posedness of the Maxwell-Dirac system in two space dimensions. (With P. D'Ancona.) Journal of Functional Analysis Volume 260, Issue 8, 15 April 2011, Pages 2300-2365
  7. Product estimates for wave-Sobolev spaces in 1+1 and 1+2 dimensions. (With P. D'Ancona and D. Foschi.) In "Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena", Contemporary Mathematics, vol. 526, Amer. Math. Soc., Providence, RI, 2010, pp. 125-150
  8. Remarks on regularity and uniqueness of the Dirac-Klein-Gordon equations in 1d. (With A. Tesfahun.) NoDEA: Nonlinear Differential Equations and Applications Volume 17, Number 4, 2010, pp. 453-465
  9. On the Maxwell-Klein-Gordon equations in Lorenz gauge. (With A. Tesfahun.) Proceedings of the International Congress of Mathematical Physics 2009. ISBN 978-981-4304-62-7
  10. Null structure and almost optimal local well-posedness of the Maxwell-Dirac system. (With P. D'Ancona and D. Foschi.) American Journal of Mathematics Volume 132, Number 3, June 2010, pp. 771-839
  11. Finite-energy global well-posedness of the Maxwell-Klein-Gordon equations in Lorenz gauge. (With A. Tesfahun.) Communications in PDE 35 (2010) no. 6, 1029-1057
  12. Low regularity well-posedness for some nonlinear Dirac equations in one space dimension. (With A. Tesfahun.) Differential Integral Equations 23 (2010) no. 3-4, 265-278
  13. 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
  14. Anisotropic bilinear L2 estimates related to the 3D wave equation. IMRN (2008). pdf.
  15. 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.
  16. 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.
  17. Global well-posedness below the charge norm for the Dirac-Klein-Gordon system in one space dimension. IMRN (2007). pdf.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. Almost optimal local well-posedness of the Klein-Gordon-Maxwell system in 1+4 dimensions. Communications in PDE 27 (2002), 1183-1227. pdf
  24. Bilinear estimates and applications to nonlinear wave equations. (With Sergiu Klainerman.) Commun. Contemp. Math. 4 (2002), 223-295. pdf
  25. On an estimate for the wave equation and applications to nonlinear problems. Differential and Integral Equations 2 (2002), 213-236. pdf
  26. 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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