## Projektseminar (Functional Analysis): Inequalities

Wintersemester 2015/16

Time and Place

Type: |
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PJSE 2 std. | Mo 9:45-11:15 | SR08 | 5.10 |

Topics

In this seminar we would like to discuss some classical inequalities with important applications
in analysis like dispersive estimates, global existence and blow-up for nonlinear PDEs etc. For example,

Hanner [LL], Rearrangement [LL], Hausdorff-Young [LL], Hardy-Littlewood-Sobolev [LL], Sobolev inequalites [LL], Rellich [LL], Poincare [LL], Strichartz [LP]These are just some possibilites and we are open to suggestions from students as well!

Presentations

Date: |
Title: |
Speaker: |
References: |

16.11 | Poincaré inequalities | Christopher Rieser | [LL], see also the errata |

23.11 | Kato's inequality | Alexis Aivaliotis | [LL,Ha] |

30.11 | Harnack's inequality | Mateusz Piorkowski | [GT,PW] |

11.01 | Eigenvalue inequalities of Hermitian matrices and Wigner's semicircle law | Peter Mühlbacher | [TT] |

18.01 | Embedding theorems | Markus Holzleitner | [LL] |

25.01 | Cwikel-Lieb-Rosenblum type inequalities | Aleksey Kostenko | [S] |

References:

- D. Gilbarg and N.S. Trudinger,
*Elliptic Partial Differential Equations of Second Order*, 2nd ed., Springer, New York, 1998. - F. Haslinger,
*The d-bar Neumann Problem and Schrödinger Operators*, De Gryter, Berlin, 2014 - E. Lieb and M. Loss,
*Analysis*, 2nd ed., GSM 14, AMS, Providence, 2001 - F. Linares und G. Ponce,
*Introduction to Nonlinear Dispersive Equations*, 2nd ed., Springer, New York, 2015 - M.H. Potter and H.F. Weinberger,
*Maximum principles in differential equations*, Prentice-Hall, 1967. - B. Simon,
*Trace Ideals and Their Applications*, Amer. Math. Soc., Providence, 2005. - T. Tao, Topics in random matrix theory, Amer. Math. Soc., Providence, 2013

Course assessment

Preparation and presentation of a chosen topic. Active participation during the course.

Audience

Majors in Mathematics (master program, code MANS), Physics, ...

Auf Ihr Kommen freuen sich Aleksey Kostenko und Gerald Teschl