## Olli Saari

Mathematisches Institut |

Endenicher Allee 60 |

D - 53115 Bonn |

Office: 3.012 |

Tel: +49 228 73-62338 |

E-mail: saari at math dot uni-bonn dot de |

I am a post-doc in the Analysis and PDE group at University of Bonn.

My research interests are in harmonic analysis and PDE,
and a brief summary of my work is

1. Analysis of time dependent problems. I have worked on regularity and properties of solutions to certain conservation laws, parabolic and p-parabolic equations. I am interested in analysis in evolving domains with applications to boundary behavior of solutions to PDE.

2. Methods from non-linear potential theory. In particular extending methods based on energy quantities and maximum principle to time dependent problems (non-linear heat potential theory). I focus on theory of capacities and applications to problems in pure analysis.

3. Maximal functions. I have spent some time on studying smoothness of maximal functions in the Sobolev sense. I care particularly much about possible applications of Fourier analysis and potential theory. I am interested in aspects of the so-called end-point regularity question.

4. Linear and bilinear Fourier multipliers. This includes maximal dilates of Fourier multipliers and their applications. I am also interested in non-smooth problems featuring simple geometric assumptions such as convexity.

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