Moritz Egert

   Moritz Egert


Maître de conférences

Équipe Analyse Harmonique


Mathématiques
Bât. 307
Université Paris-Sud
91405 Orsay Cedex
France


Email:
Office : 2G3
Phone : (+33) 1 69 15 32 48


Pour le cycliste Moritz Egert, cliquez ici!


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 Haller-Dintelmann 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 non-autonomous 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. Lp-estimates for the square root of elliptic systems with mixed boundary conditions, J. Differential Equations 265 (2018), no. 4, 1279-1323.

2. Non-local self-improving properties: A functional analytic approach. with P. Auscher and S. Bortz and O. Saari, Tunisian J. Math. 1 (2019), no. 2, 151-183.

3. Non-local Gehring lemmas. with P. Auscher and S. Bortz and O. Saari, 46 pages, submitted 2017.

4. On regularity of weak solutions to parabolic systems. with P. Auscher and S. Bortz and O. Saari, 23 pages, accepted for publication in J. Math. Pures Appl.

5. On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity. with P. Auscher, 22 pages, submitted 2017.

6. The Dirichlet problem for second order parabolic operators in divergence form. with P. Auscher and K. Nyström, 36 pages, accepted for publication in J. Éc. polytech. Math.

7. L2 well-posedness 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.

8. 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, 729-743.

9. On non-autonomous maximal regularity for elliptic operators in divergence form, with P. Auscher, Arch. Math. 107 (2016), no. 3, 271–284.

10. Mixed boundary value problems on cylindrical domains, with P. Auscher, Adv. Differential Equ. 22 (2017), no.~1/2, 101-168

11. Hardy's inequality for functions vanishing on a part of the boundary, with Haller-Dintelmann and J. Rehberg, Potential Anal. 43 (2015), no.1, 49-78.

12. The Kato Square Root Problem for Mixed Boundary Conditions, with R. Haller-Dintelmann and P. Tolksdorf, J. Funct. Anal. 267 (2014), no.5, 1419-1461.

13. The Kato Square Root Problem follows from an Extrapolation Property of the Laplacian, with R. Haller-Dintelmann and P. Tolksdorf, Publ. Math. 61 (2016), no. 2, 451-483.

14. Convergence of subdiagonal Padé approximations to C0-semigroups, with J. Rozendaal, J. Evol. Equ. 13 (2013), no.4, 875-895.


Work in progress

Boundary value problems for elliptic systems with block structure: the ultimate results, with P. Auscher.


Interpolation theory for functions with partially vanishing trace on Ahlfors regular open sets, with S. Bechtel.


Thesis

On Kato's conjecture and mixed boundary conditions, PhD thesis, Sierke Verlag, Göttingen, 2015, ISBN: 978-3-86844-719-4. (Ask me for a copy, if you are interested!)


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
2. The Kato problem for parabolic systems in divergence form. Harmonic Analysis of Elliptic and Parabolic Partial Differential Equations, CIRM Luminy, 27 april 2018
3. How half-order time derivatives help us to better understand parabolic equations, Langenbach Seminar, WIAS Berlin, 28 february 2018
4. What do we know about the Kato problem for Dirichlet boundary conditions on open sets? Harmonic Analysis in Winter, ICMAT Madrid, 10 january 2018
5. How half-order time derivatives help us to better understand parabolic equations, Colloquium on Analysis and Applications, TU Delft, 30 november 2017
6. Régularité parabolique par une approche non locale, Rentrée de l'équipe d'analyse harmonique, Université Paris-Sud, 17 october 2017
7. Hölder continuity in time for weak solutions to parabolic systems : A non-local approach, ANR HAB Meeting Lyon, 14 june 2017
8. Équations paraboliques non-autonomes par un système de Cauchy-Riemann, Le séminaire d’EDP-physique mathématique, Université Bordeaux, 9 may 2017
9. Cauchy-Riemann system for non-autonomous parabolic PDEs, Operator semigroups in analysis: modern developments, Bedlewo, Pologne, 24 avril
10. Systèmes de Cauchy-Riemann et EDPs du second ordre,Séminaire EDP-Analyse Lyon, Université Lyon 1, 4 april 2017
11. Cauchy-Riemann systems for second order partial differential equations, Postdoc seminar, MSRI Berkeley, 14 march 2017
12. Non-autonomous maximal regularity for elliptic operators in divergence form, Journée d'Analyse Non Linéaire, Université Paris-Sud, 6 June 2016
13. Non-autonomous maximal regularity for divergence-form operators, Analysis Seminar, Birmingham School of Mathematics, 21 March 2016
14. Hardy's inequality for functions vanishing on a part of the boundary, Analysis and Stochastics Seminar, Uppsala Universitet, 16 February 2016
15. On Hardy's inequality for functions with partially vanishing trace, Harmonic Analysis Seminar, Université Paris-Sud, 19 January 2016
16. On Kato's Square Root Problem, WIAS Berlin, 11 February 2015
17. On an elliptic mixed boundary value problem, TU Delft, 13 November 2014
18. Square Roots of Elliptic Systems, Harmonic Analysis Seminar of the Louisiana State University, Baton Rouge, USA, 3 October 2012

1. Mixed boundary value problems on cylindrical domains, PDE 2015, WIAS Berlin, 2 December 2015
2. Polynomial Decay of Bounded C0-semigroups on Hilbert Spaces, Final workshop of the 16th Internet Seminar on Evolution Equations, Blaubeuren, Germany, 10 June 2013
3. The Kato Square Root Problem for Mixed Boundary Conditions, Symposium "Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics", Herrnhut, Germany, 3 June 2013
4. Rational Approximations of Semigroups without Scaling and Squaring, Final workshop of the 15th Internet Seminar on Evolution Equations, Blaubeuren, Germany, 8 June 2012
5. Feedback Stabilizability of Delay Systems in Banach Spaces, Final workshop of the 14th Internet Seminar on Evolution Equations, Blaubeuren, Germany, 10 June 2011
6. Barenblatt's solution to the Porous Medium Equation, Final workshop of the 13th Internet Seminar on Evolution Equations, Kacov, Czech Republic, 18 June 2010

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...)