# Sigmund Selberg

### Professor

Department of Mathematical Sciences

Norwegian University of Science and Technology

## Contact information

Address: | Institutt for matematiske fag NTNU Alfred Getz' vei 1 N-7491, Trondheim Norway |
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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 |
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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 |

## Research

#### Submitted:

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

#### Published:

- 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 - 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 - Dispersive estimate for the 1D Schrödinger equation with a steplike potential. (With P. D'Ancona.)
*Journal of Differential Equations.*252 (2012) 1603-1634 - Atlas of products for wave-Sobolev spaces on
**R**^{1+3}. (With P. D'Ancona and D. Foschi.)*Transactions of the AMS.*364 (2012), 31-63 - Bilinear Fourier restriction estimates related to the 2d wave equation.
*Advances in Differential Equations*Volume 16, Numbers 7-8, 2011, Pages 667-690 - 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 - 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 - 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 - 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
- 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 - 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 - 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 - 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
- Anisotropic bilinear
*L*^{2}estimates related to the 3D wave equation.*IMRN*(2008). pdf. - 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. - 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. - Global well-posedness below the charge norm for the Dirac-Klein-Gordon system in one space dimension.
*IMRN*(2007). pdf. - 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. - 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. - 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. - 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. - 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. - Almost optimal local well-posedness of the Klein-Gordon-Maxwell system in 1+4 dimensions.
*Communications in PDE***27**(2002), 1183-1227. pdf - Bilinear estimates and applications to nonlinear wave equations. (With Sergiu Klainerman.)
*Commun. Contemp. Math.***4**(2002), 223-295. pdf - On an estimate for the wave equation and applications to nonlinear problems.
*Differential and Integral Equations***2**(2002), 213-236. pdf - Remark on the optimal regularity for equations of wave maps type. (With Sergiu Klainerman.)
*Communications in PDE***22**(1997), 901-918. pdf