Moritz Egert
Harmonic Analysis & PDEs

Prof. Dr. Moritz Egert

Working area(s)

Analysis

Contact

work +49 6151 16-21477

Work S2|15 407
Schlossgartenstraße 7
64289 Darmstadt

Research Interests

I am interested in Harmonic Analysis and Functional Calculus and their applications to Partial Differential Equations (PDEs), in particular to elliptic and parabolic Divergence Form Operators. Click here (opens in new tab) for a more detailed CV.

Teaching in the Winter Term 22/23

  • Partial Differential Equations I (in English)
  • Proseminar (in English)

If you are interested in a Bachelor's or Master's thesis in my group, feel free to contact me.

Office hour: By appointment (contact me via email).

Up-to-date versions of my publications can be found on HAL and arXiv. Inaccuracies that are pointed out to me after publication are usually corrected in these versions.

Research Papers and Preprints

  • The Kato square root problem for weighted parabolic operators (with A. Ataei and K. Nyström), 27 pages, preprint 2022. arXiv
  • Carleson Conditions for Weights: The quantitative small constant case (with S. Bortz and O. Saari), 15 pages, preprint 2022. arXiv
  • Hardy spaces for boundary value problems of elliptic systems with block structure (with P. Auscher), 17 pages, J. Geom. Anal. (2021).arXiv
  • Boundary value problems and Hardy spaces for elliptic systems with block structure (with P. Auscher), 245 pages, submitted 2020.arXiv Talk Lancaster (opens in new tab) (2021)
  • Note on time-regularity for weak solutions to parabolic systems of p-Laplace type (with S. Bortz), Proc. Amer. Math. Soc. 149 (2021), no.4, 1677–1685.arXiv
  • Sobolev contractivity of gradient flow maximal functions (with S. Bortz and O. Saari) 23 pages, submitted 2019.arXiv
  • The Kato square root problem on locally uniform domains (with S. Bechtel and R. Haller-Dintelmann) Adv. Math. 375 (2020).arXiv
  • On p-elliptic divergence form operators and holomorphic semigroups, J. Evol. Equ. 20 (2020), no.3, 705-724.arXiv Talk in Bad Herrenalb (opens in new tab) (2019)
  • Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets (with S. Bechtel), J. Fourier Anal. Appl. 25 (2019), no. 5, 2733-2781.arXiv
  • Lp-estimates for the square root of elliptic systems with mixed boundary conditions, J. Differential Equations 265 (2018), no. 4, 1279-1323. arXiv
  • 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.arXiv
  • Non-local Gehring lemmas in spaces of homogeneous type and applications (with P. Auscher and S. Bortz and O. Saari), J. Geom. Anal. 30 (2019), no.4, 3760-3805.arXiv
  • 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), 216-243.arXiv Colloquium Talk WIAS Berlin (opens in new tab) (2018)
  • On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi- Nash-Moser regularity (with P. Auscher), Anal. PDE 13 (2020), no.6, 1605-1632.arXiv
  • 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. arXiv
  • L2 well-posedness of boundary value problems for parabolic systems with measurable coefficients (with P. Auscher and K. Nyström), J. Eur. Math. Soc. (JEMS) 22 (2020), no.9, 2943-3058.arXiv Talk in Bedlewo (opens in new tab) (2017)
  • 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.arXiv
  • On non-autonomous maximal regularity for elliptic operators in divergence form (with P. Auscher), Arch. Math. 107 (2016), no. 3, 271–284.arXiv Colloquium Talk WIAS Berlin (opens in new tab) (2018)
  • Mixed boundary value problems on cylindrical domains (with P. Auscher), Adv. Differential Equ. 22 (2017), no.1/2, 101-168. arXiv Talk in Delft (opens in new tab) (2014)
  • 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.arXiv
  • 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.arXiv Talk in Herrnhut (opens in new tab) (2013)
  • The Kato Square Root Problem follows from an Extrapolation Property of the Laplacian (with R. Haller-Dintelmann and P. Tolksdorf), Publ. Mat. 60 (2016), no. 2, 451-483.arXiv
  • Convergence of subdiagonal Padé approximations to C0-semigroups (with J. Rozendaal), J. Evol. Equ. 13 (2013), no.4, 875-895.arXiv

Books/Thesis

Things of Interest