Research interestsI am interested in the harmonic analysis and operator theory of differential operators, in particular elliptic and parabolic systems in divergence form. In my PhD Thesis, supervised by Robert HallerDintelmann at TU Darmstadt, I solved the Kato Square Root Problem for systems with mixed Dirichlet/Neumann boundary conditions posed on rough domains beyond the Lipschitz class. Besides harmonic analysis and operator theory, this required to bring into play a third, exciting flavor: geometric measure theory. More recently, I worked on classical elliptic and parabolic boundary value problems on the upper half space and on nonautonomous maximal regularity questions. Other research interests of mine lie in potential theory, in particular trace and extension theorems for Sobolev functions and Hardy's inequality. I have also worked on numerical approximation schemes for strongly continuous semigroups. My full scientific CV can be found here (in French).
Publications
1.
Nonlocal selfimproving properties: A functional analytic approach.
with P. Auscher and S. Bortz and O. Saari, 18 pages, submitted 2017.
2.
Nonlocal Gehring lemmas.
with P. Auscher and S. Bortz and O. Saari, 46 pages, submitted 2017.
3.
On regularity of weak solutions to parabolic systems.
with P. Auscher and S. Bortz and O. Saari, 19 pages, submitted 2017.
4.
On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgiNashMoser regularity.
with P. Auscher, 22 pages, submitted 2017.
5.
The Dirichlet problem for second order parabolic operators in divergence form.
with P. Auscher and K. Nyström, 26 pages, submitted 2016.
6. L2 wellposedness of boundary value problems for parabolic systems with measurable coefficients,
with P. Auscher and K. Nyström, 83 pages, submitted 2017.
7. Characterizations of Sobolev functions that vanish on a part of the
boundary, with P. Tolksdorf, Discrete Contin. Dyn. Syst. Ser. S 10 (2017), no. 4, 729743.
8. On nonautonomous maximal regularity for elliptic operators
in divergence form, with P. Auscher, Arch. Math. 107 (2016), no. 3, 271–284.
9. Mixed boundary value problems on
cylindrical domains, with P. Auscher, Adv. Differential Equ. 22 (2017), no.~1/2, 101168
10. Hardy's inequality for functions vanishing on
a part of the boundary, with HallerDintelmann and J.
Rehberg, Potential Anal. 43 (2015), no.1, 4978.
11. The Kato Square Root Problem for Mixed
Boundary Conditions, with R. HallerDintelmann and P.
Tolksdorf, J. Funct. Anal. 267 (2014), no.5, 14191461.
12. The
Kato Square Root Problem follows from an Extrapolation
Property of the Laplacian, with R. HallerDintelmann and
P. Tolksdorf, Publ. Math. 61 (2016), no. 2, 451483. 13. Convergence of subdiagonal Padé approximations to C0semigroups, with J. Rozendaal, J. Evol. Equ. 13 (2013), no.4, 875895. ThesisOn Kato's conjecture and mixed boundary conditions, PhD thesis, Sierke Verlag, Göttingen, 2015, ISBN: 9783868447194. (Ask me for a copy, if you are interested!)
Teaching experienceI worked as an undergraduate teaching assistant for several analysis courses at TU Darmstadt permanently between 2008 and 2011 and as a graduate teaching assistant between 2012 and 2014. I have been a coordinator for projects of the Internet Seminar on Evolution Equations: In 2014 I have offered the project The Dirichlet Laplacian as generator on spaces of continuous functions and in 2015 the project Fractional powers and Kato's conjecture (both jointly with Robert HallerDintelmann).
Invited talks
1. Équations paraboliques nonautonomes par un système de CauchyRiemann, Le séminaire d’EDPphysique mathématique, Université Bordeaux, 9 may 2017
Contributed talks1. Mixed boundary value problems on cylindrical domains,
PDE 2015, WIAS Berlin, 2 December 2015
Things of interestFollow my "career" as a racing cyclist here (in German). The current edition of the Internet Seminar on Evolution Equations deals with parabolic operators with bounded and unbounded coefficients. Here, it only takes you a minute to write a mathematical paper (Claim: 5 is less than 7. Proof: One direction is obvious. So, let us prove the converse...) 
Département de Mathématiques
Bâtiment 425 Faculté des Sciences d'Orsay Université ParisSud F91405 Orsay Cedex Tél. : +33 (0) 169157956
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