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).
18. Sobolev contractivity of gradient flow maximal functions, with S. Bortz and O. Saari, 23 pages, submitted 2019. 17. The Kato square root problem on locally uniform domains, with S. Bechtel and R. HallerDintelmann, 31 pages, submitted 2019. 16. On pelliptic divergence form operators and holomorphic semigroups, 17 pages, J. Evol. Equ. (2019. 15. Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets, with S. Bechtel, J. Fourier Anal. Appl. 25 (2019), no. 5, 27332781
14.
Lpestimates for the square root of elliptic systems with mixed boundary conditions,
J. Differential Equations 265 (2018), no. 4, 12791323.
13.
Nonlocal selfimproving properties: A functional analytic approach.
with P. Auscher and S. Bortz and O. Saari, Tunisian J. Math. 1 (2019), no. 2, 151183.
12.
Nonlocal Gehring lemmas in spaces of homogeneous type and applications.
with P. Auscher and S. Bortz and O. Saari, 46 pages, J. Geom. Anal. (2019).
11.
On regularity of weak solutions to linear parabolic systems with measurble coefficients.
with P. Auscher and S. Bortz and O. Saari, J. Math. Pures Appl. 121 (2019), 216243.
10.
On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgiNashMoser regularity.
with P. Auscher, 22 pages, accepted for publication in Analysis & PDE .
9.
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.
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.
6. On nonautonomous maximal regularity for elliptic operators
in divergence form, with P. Auscher, Arch. Math. 107 (2016), no. 3, 271–284.
5. Mixed boundary value problems on
cylindrical domains, with P. Auscher, Adv. Differential Equ. 22 (2017), no.~1/2, 101168
4. Hardy's inequality for functions vanishing on
a part of the boundary, with HallerDintelmann and J.
Rehberg, Potential Anal. 43 (2015), no.1, 4978.
3. The Kato Square Root Problem for Mixed
Boundary Conditions, with R. HallerDintelmann and P.
Tolksdorf, J. Funct. Anal. 267 (2014), no.5, 14191461.
2. 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. 1. 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. The Kato estimate for weighted parabolic operators, with P. Auscher, K. Nyström, C. Rios.
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 2019/2020: Cours d'analyse pour la PCSO For a complete list, view my full scientific CV here (in French). 1. On pelliptic operators and holomorphic semigroups. Parabolic Evolution Equations, Harmonic Analysis and Spectral Theory, Bad Herrenalb, 8 may 2019
1. pelliptic operators and heat semigroups. Harmonic Analysis and PDE, Helsinki, 5 juin 2019 
Département de Mathématiques
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