Hey there! I 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).
1. Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets, with S. Bechtel, 42 pages, submitted 2018.
2.
Lpestimates for the square root of elliptic systems with mixed boundary conditions,
J. Differential Equations 265 (2018), no. 4, 12791323.
3.
Nonlocal selfimproving properties: A functional analytic approach.
with P. Auscher and S. Bortz and O. Saari, Tunisian J. Math. 1 (2019), no. 2, 151183.
4.
Nonlocal Gehring lemmas in spaces of homogeneous type and applications.
with P. Auscher and S. Bortz and O. Saari, 40 pages, submitted 2017.
5.
On regularity of weak solutions to linear parabolic systems with measurble coefficients.
with P. Auscher and S. Bortz and O. Saari, 28 pages, to appear in J. Math. Pures Appl.
6.
On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgiNashMoser regularity.
with P. Auscher, 22 pages, submitted 2017.
7.
The Dirichlet problem for second order parabolic operators in divergence form.
with P. Auscher and K. Nyström, J. Éc. polytech. Math. 5 (2018), 407–441.
8. L2 wellposedness of boundary value problems for parabolic systems with measurable coefficients,
with P. Auscher and K. Nyström, 83 pages, accepted for publication in J. Eur. Math. Soc.
9. 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.
10. On nonautonomous maximal regularity for elliptic operators
in divergence form, with P. Auscher, Arch. Math. 107 (2016), no. 3, 271–284.
11. Mixed boundary value problems on
cylindrical domains, with P. Auscher, Adv. Differential Equ. 22 (2017), no.~1/2, 101168
12. Hardy's inequality for functions vanishing on
a part of the boundary, with HallerDintelmann and J.
Rehberg, Potential Anal. 43 (2015), no.1, 4978.
13. The Kato Square Root Problem for Mixed
Boundary Conditions, with R. HallerDintelmann and P.
Tolksdorf, J. Funct. Anal. 267 (2014), no.5, 14191461.
14. 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. 15. Convergence of subdiagonal Padé approximations to C0semigroups, with J. Rozendaal, J. Evol. Equ. 13 (2013), no.4, 875895. Work in progressBoundary value problems for elliptic systems with block structure: the ultimate results, with P. Auscher.
ThesisOn Kato's conjecture and mixed boundary conditions, PhD thesis, Sierke Verlag, Göttingen, 2015, ISBN: 9783868447194. (A steadily updated and corrected version is available here)
Winter 2017/2018: Cours et TD d'analyse pour la PCSO Summer 2018: TD Analyse Fourier (Math 256) for David Harrari's course. Summer 2018: TD Analyse Complex (Math 308) for Joël Merker's course. For a complete list, view my full scientific CV here (in French). 1. The Kato problem for parabolic systems in divergence form. Research Term on Real Harmonic Analysis and Its Applications to Partial Differential Equations and Geometric Measure Theory, ICMAT Madrid, 16 may 2018
1. Mixed boundary value problems on cylindrical domains,
PDE 2015, WIAS Berlin, 2 December 2015
Follow my "career" as a racing cyclist here (in German). The current edition of the Internet Seminar on Evolution Equations focusses on functional calculus. 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...) 
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