Publications
Projects
Awards
Academy
News
Prof. Dr. Hannes Meinlschmidt
Email • PhD in mathematics, TU Darmstadt
intersection of (optimal) control and optimization with the analysis of PDEs
Assistant Professor | Senior Scientist
Room 03.330 | FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
Friedrich-Alexander-Universität Erlangen-Nürnberg
Naturwissenschaftliche Fakultät. Department Mathematik
ORCID | Google Scholar | Personal site | X
I am an assistant professor (W1) at the Chair for Dynamics, Control, Machine Learning and Numerics at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg since March 2021.
I am working on optimal control of partial differential equations and applied analysis in general.
I obtained both my Diploma (Oct 2011) and PhD (March 2017) in mathematics at TU Darmstadt, Germany; my PhD supervisor was Stefan Ulbrich.
I then moved to RICAM in Linz, Austria, for a PostDoc position in the “Optimization and Optimal Control” group of Karl Kunisch, in September 2017.
• PhD Thesis: “Analysis and Optimal Control of Quasilinear Parabolic Evolution Equations on Rough Domains” (March 2017)
See more: News
Research interests
My research interests concern problems at the intersection of (optimal) control and optimization with the analysis of PDEs.
This includes
• regularization aspects on the optimization side
• regularity theory for elliptic and parabolic evolution equations on the analysis side
The research questions I consider are motivated mostly by
• optimal control problems subject to strongly nonlinear (coupled systems of) time- dependent PDEs,
• real-world applications with nonsmooth data
Projects
• Renormalized Solutions in der Optimalsteuerung von Evolutionsgleichungen (2025 – 2028)
• CIN-PDE: Control, inversion and numerics for Partial Differential Equations (2022 – 2025)
Awards
• Preis für hervorragende wissenschaftliche Leistungen (2018) TU Darmstadt
Award for outstanding scientific achievements for the best PhD dissertation at the Department of Mathematics at TU Darmstadt in 2017
Academy
• Lecture notes: A primer on functional Analytic methods for PDEs
• WS 22/23: Lecture „Optimization with PDEs”
• WS 22/23: Seminar on „Interpolation theory and function spaces”
• SS 21/22: Partielle Differentialgleichungen I
• WS 21/22: Partielle Differentialgleichungen II
• WS 20/21: A Primer on Functional Analytic Methods for PDE. Seminar “Evolution Equations”
News / Initiatives
Poster: Parabolic Problems Arising in Real-World Applications
Authors: Hannes Meinlschmidt
Date: March, 2021
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Publications
2025
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Optimal control of quasilinear parabolic PDEs with gradient terms and pointwise constraints on the gradient of the state
In: Mathematical Control and Related Fields 15 (2025), p. 1284-1319
ISSN: 2156-8472
DOI: 10.3934/mcrf.2025037
BibTeX: Download
2024
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Hölder regularity for domains of fractional powers of elliptic operators with mixed boundary conditions
In: Pure and Applied Functional Analysis 9 (2024), p. 169-194
ISSN: 2189-3764
BibTeX: Download - , , :
GLOBAL-IN-TIME SOLUTIONS AND HÖLDER CONTINUITY FOR QUASILINEAR PARABOLIC PDES WITH MIXED BOUNDARY CONDITIONS IN THE BESSEL DUAL SCALE
In: Evolution Equations and Control Theory 13 (2024), p. 1250-1286
ISSN: 2163-2480
DOI: 10.3934/eect.2024025
BibTeX: Download - , , :
A variational approach to Continuous Time Dynamic Models
In: Mark Stemmler, Wolfgang Wiedermann, Francis Huang (ed.): Dependent Data in Social Sciences Research - Forms, Issues and Methods of Analysis (second edition), Cham: Springer, 2024
ISBN: 978-3-031-56317-1
DOI: 10.1007/978-3-031-56318-8_5
BibTeX: Download
2021
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Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations
In: Journal of Differential Equations 280 (2021), p. 375-404
ISSN: 0022-0396
DOI: 10.1016/j.jde.2021.01.032
BibTeX: Download
2020
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On the numerical range of second-order elliptic operators with mixed boundary conditions in Lp
In: Journal of Evolution Equations (2020)
ISSN: 1424-3199
DOI: 10.1007/s00028-020-00642-6
BibTeX: Download - , :
Optimal control of an energy-critical semilinear wave equation in 3D with spatially integrated control constraints
In: Journal De Mathematiques Pures Et Appliquees 138 (2020), p. 46-87
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2020.03.006
BibTeX: Download - , , :
Regularization for optimal control problems associated to nonlinear evolution equations
In: Journal of Convex Analysis 27 (2020), p. 443-485
ISSN: 0944-6532
URL: https://www.heldermann.de/JCA/JCA27/JCA272/jca27025.htm
BibTeX: Download - , , :
Optimal control of an abstract evolution variational inequality with application in homogenized plasticity
In: Journal of Nonsmooth Analysis and Optimization 1 (2020)
ISSN: 2700-7448
DOI: 10.46298/jnsao-2020-5800
URL: https://jnsao.episciences.org/6467
BibTeX: Download
2019
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Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions
In: Annali Di Matematica Pura Ed Applicata 198 (2019), p. 1227-1241
ISSN: 0373-3114
DOI: 10.1007/s10231-018-0818-9
BibTeX: Download
2018
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The full Keller-Segel model is well-posed on nonsmooth domains
In: Nonlinearity 31 (2018), p. 1560-1592
ISSN: 0951-7715
DOI: 10.1088/1361-6544/aaa2e1
BibTeX: Download
2017
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Analysis and Optimal Control of Quasilinear Parabolic Evolution Equations in Divergence Form on Rough Domains (Dissertation, 2017)
BibTeX: Download - , , :
Optimal control of the thermistor problem in three spatial dimensions, part 1: Existence of optimal solutions
In: SIAM Journal on Control and Optimization 55 (2017), p. 2876-2904
ISSN: 0363-0129
DOI: 10.1137/16M1072644
BibTeX: Download - , , :
Optimal control of the thermistor problem in three spatial dimensions, part 2: Optimality conditions
In: SIAM Journal on Control and Optimization 55 (2017), p. 2368-2392
ISSN: 0363-0129
DOI: 10.1137/16M1072656
BibTeX: Download
2016
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Hölder-estimates for non-autonomous parabolic problems with rough data
In: Evolution Equations and Control Theory 5 (2016), p. 147-184
ISSN: 2163-2480
DOI: 10.3934/eect.2016.5.147
BibTeX: Download
