Research

On this page you can find my publication list, talks that I gave at conferences and in seminars, as well as information on a book that I wrote.

Publications Link to heading

My articles can usually be found in their newest version on my arXiv page.

Published Link to heading

The following articles were already accepted for publication in peer-reviewed journals.

1. Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets, with M. Egert. Appeared in J. Fourier Anal. Appl. in 2019. arXiv link, journal link.
2. The Kato square root problem on locally uniform domains, with M. Egert and R. Haller. Appeared in Adv. Math. in 2020. arXiv link, journal link.
3. The extension problem for fractional Sobolev spaces with a partial vanishing trace condition, appeared in Arch. Math. in 2021. arXiv link, journal link.
4. Off-diagonal bounds for the Dirichlet-to-Neumann operator, with E.M. Ouhabaz. Appeared in J. Math. Anal. Appl. in 2024. arXiv link, journal link.
5. $L^p$ bounds for square roots of elliptic systems on open sets. Appeared in J. Differential Equations in 2024. arXiv link, journal link.
6. Sobolev extension operators for functions with partially vanishing trace, with R.M. Brown, R. Haller, and P. Tolksdorf. To appear in Ann. Inst. Fourier. arXiv link, journal link.
7. Counterexamples to maximal regularity for operators in divergence form, with C. Mooney and M. Veraar. Appeared in Arch. Math. in 2024. arXiv link, journal link.
8. Weighted non-autonomous $L^q(L^p)$ maximal regularity for complex systems under mixed regularity in space and time. Appeared in J. Differential Equations in 2024. arXiv link, journal link.

Proceedings Link to heading

9. Around maximal regularity for Navier–Stokes Equations, with C. Bui and P. Kunstmann. Appeared in Panorama et Synthèses in 2024, proceedings link.

Preprints Link to heading

The following articles are in preparation or submitted.

10. An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems, with M. Veraar. Submitted in 2023. arXiv link.
11. Hardy spaces on open sets adapted to mixed boundary conditions, with T. Böhnlein. Submitted in 2024. arXiv link.
12. A second order approach to the Kato square root problem on open sets, with C. Hutcheson, T. Schmatzler, T. Tasci, and M. Wittig. Student project in the scope of ISEM27. arXiv link.
13. An extended variational setting for critical SPDEs with Lévy noise, with F. Germ and M. Veraar. arXiv link.

Book Link to heading

I wrote a book entitled Square Roots of Elliptic Systems in Locally Uniform Domains that appeared in Birkhäuser’s series Linear Operators and Linear Systems (volume 303). It is based on my PhD thesis.

Talks Link to heading

Conference talks Link to heading

Seminar talks Link to heading

PhD defense Link to heading

For an overview of the topics in my PhD thesis, you can have a look on the slides that I presented during my PhD defense.

Prices & Awards Link to heading

• 3rd best talk at the Oberwolfach Seminar 2247b, awarded by a bottle of Saint-Émilion wine
• 1st place best presentation award ISEM27 (supervision rôle), awarded by a bottle of Louis Constant champagne