## Prof. Dr. Robert Haller

### Working area(s)

### Contact

haller@mathematik.tu-...

work +49 6151 16-21478

fax +49 6151 16-21483

Work
S2|15 422

Schlossgartenstraße 7

64289
Darmstadt

## Office hour

During summer term 2024: Mo., 10:00 – 11:00 in S2 15/422

During the semester break: by appointment.

- Regularity theory for elliptic and parabolic PDEs
- Maximal parabolic regularity
- Divergence form operators with mixed boundary conditions
- Non-smooth coefficients and domains
- Kato square root conjecture
- Transmission problems on polyhedral domains
- Quasi-linear parabolic equations
- Ornstein-Uhlenbeck operators
- Kernel estimates, especially Gaussian and Poisson bounds

- Operator theory
- Sectorial operators in Banach spaces
- H
^{∞}-functional calculus - R-bounded operator families
- Sums and products, theorems of Dore-Venni type

- Operator semigroups
- Harmonic analysis
- Spectral theory

**Papers already published or accepted**

- F. Brandt, K. Disser, R. Haller-Dintelmann, and M. Hieber, “Rigorous analysis and dynamics of Hibler's sea ice model”.

J. Nonlinear Sci.**32**(2022), no. 4, paper no. 50, 26 pp.

ArXiv: 2104.01336 - A.F.M. ter Elst, R. Haller-Dintelmann, J. Rehberg, and P. Tolksdorf, “On the L
^{p}- theory for second order elliptic operators in divergence form with complex coefficients”.

J. Evol. Equ.**21**(2021), no. 4, 3963-4003.

ArXiv:1903.06692 - S. Bechtel, M. Egert, and R. Haller-Dintelmann, “The Kato square root problem on locally uniform domains”.

Adv. Math.**320**(2020).

ArXiv:1902.03957 - R. Haller-Dintelmann, H. Meinlschmidt, and W. Wollner, “Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions”.

Ann. Mat. Pura Appl. (4)**198**(2019), no. 4, 1227-1241. - R. Haller-Dintelmann, A. Jonsson, D. Knees, and J. Rehberg, “On elliptic and parabolic regularity for mixed boundary value problems”.

Math. Methods Appl. Sci.**39**(2016), no. 17, 5007-5026.

ArXiv:1310.3679, WIAS-Preprint no. 1706 (opens in new tab). - M. Egert, R. Haller-Dintelmann, and P. Tolksdorf, “The Kato Square Root Problem follows from an Extrapolation Property of the Laplacian”.

Publ. Mat.**60**(2016), no. 2, 451-483.

arXiv:1311.0301. - M. Egert, R. Haller-Dintelmann, and J. Rehberg, “Hardy's inequality for functions vanishing on a part of the boundary”.

Potential Anal.**43**(2015), no. 1, 49-78.

arXiv:1405.6167. - P. Auscher, N. Badr, R. Haller-Dintelmann, and J. Rehberg, “The square root problem for second order, divergence form operators with mixed boundary conditions on L
^{p}”.

J. Evol. Equ.**15**(2015), no. 1, 165-208.

arXiv:1210.0780. - R. Haller-Dintelmann, W. Höppner, H.-C. Kaiser, J. Rehberg, and G. M. Ziegler, “Optimal elliptic regularity in Sobolev spaces near three-dimensional multimaterial Neumann vertices”.

Funct. Anal. Appl.**48**(2014), no. 3, 208-222.

WIAS-Preprint no. 1515 (opens in new tab). - M. Egert, R. Haller-Dintelmann, and P. Tolksdorf, “The Kato Square Root Problem for mixed boundary conditions”.

J. Funct. Anal.**267**(2014), no. 5, 1419-1461.

arXiv:1311.0302. - F. Ali Mehmeti, R. Haller-Dintelmann, and V. Régnier, “Dispersive waves with multiple tunnel effect on a star-shaped network”.

Discrete Contin. Dyn. Syst. Ser. S**6**(2013), no. 3, 783-791. - F. Ali Mehmeti, R. Haller-Dintelmann, and V. Régnier, “Energy flow above the threshold of tunnel effect”.

In: A. Almeida, L. Castro, and F.-O. Speck (eds.): “Advances in Harmonic Analysis and Operator Theory”, vol. 229 of Operator Theory: Advances and Applications, pp. 65-76, Birkhäuser, 2013. - F. Ali Mehmeti, R. Haller-Dintelmann, and V. Régnier, “Multiple tunnel effect for dispersive waves on a star-shaped network: an explicit formula for the spectral representation”.

J. Evol. Equ.**12**(2012), no. 3, 513-545. - F. Ali Mehmeti, R. Haller-Dintelmann, and V. Régnier, “The influence of the tunnel effect on L
^{∞}-time decay”.

In: W. Arendt, J. A. Ball, J. Behrndt, K.-H. Förster, V. Mehrmann, and C. Trunk (eds.): “Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations”, vol. 221 of Operator Theory: Advances and Applications, pp. 11-24, Birkhäuser, 2012. - R. Haller-Dintelmann and J. Rehberg, “Maximal parabolic regularity for divergence operators on distribution spaces”.

In: J. Escher, P. Guidotti, M. Hieber, P. Mucha, J. Prüss, Y. Shibata, G. Simonett, C. Walker, and W. Zajaczkowski (eds.): “Parabolic Problems – The Herbert Amann Festschrift”, pp. 313-341, Birkhäuser, 2011.

WIAS-Preprint no. 1459 (opens in new tab). - R. Haller-Dintelmann, H.-C. Kaiser, and J. Rehberg, “Direct computation of elliptic singularities across anisotropic, multi-material edges”.

J. Math. Sci. (N.Y.)**172**(2011), no. 4, 589-622.

WIAS-Preprint no. 1439 (opens in new tab). - R. Haller-Dintelmann and J. Rehberg, “Coercivity for elliptic operators and positivity of solutions on Lipschitz domains”.

Arch. Math.**95**(2010), no. 5, 457-468.

WIAS-Preprint no. 1473 (opens in new tab). - R. Haller-Dintelmann, C. Meyer, J. Rehberg, and A. Schiela, “Hölder continuity and optimal control for nonsmooth elliptic problems”.

Appl. Math. Optim.**60**(2009), 397-428.

WIAS-Preprint no. 1316 (opens in new tab). - R. Haller-Dintelmann and J. Rehberg, “Maximal parabolic regularity for divergence operators including mixed boundary conditions”.

J. Differential Equations**247**(2009), 1354-1396.

WIAS-Preprint no. 1288 (opens in new tab). - R. Haller-Dintelmann, H.-C. Kaiser, and J. Rehberg, “Elliptic model problems including mixed boundary conditions and material heterogeneities”.

J. Math. Pures Appl.**89**(2008), 25-48.

WIAS-Preprint no. 1203. - F. Ali Mehmeti, R. Haller-Dintelmann, and V. Régnier, “Expansions in generalized eigenfunctions of the weighted Laplacian on star-shaped networks”.

In: H. Amman, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, and J. von Below (eds.): “Functional Analysis and Evolution Equations – The Günter Lumer Volume”, pp. 1-16, Birkhäuser, 2008.

Preprint (opens in new tab). - R. Haller-Dintelmann, M. Hieber, and J. Rehberg, “Irreducibility and mixed boundary conditions”.

Positivity**12**(2008), no. 1, 83-91.

Preprint (opens in new tab). - R. Haller-Dintelmann and J. Wiedl, “Elliptic operators with unbounded drift coefficients on domains”.

Ulmer Seminare**11**(2006), 207-214.

Preprint (opens in new tab). - R. Haller-Dintelmann, H. Heck, and M. Hieber, “L
^{p}-L^{q}-estimates for parabolic systems in non-divergence form with VMO coefficients”.

J. London Math. Soc. (2)**74**(2006), no. 3, 717-736.

Preprint no. 2375, TU Darmstadt (opens in new tab). - R. Haller Dintelmann and J. Wiedl, “Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator”.

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)**4**(2005), 729-748. - R. Haller-Dintelmann and M. Hieber, “H
^{∞}-calculus for products of non-commuting operators”.

Math. Z.**251**(2005), 85-100. - R. Haller-Dintelmann, “An extrapolation theorem for the bounded H
^{∞}-calculus on L^{p}(Ω; X)”.

Differential Integral Equations**18**(2005), no. 3, 263-280. - R. Haller, H. Heck, and M. Hieber, “Muckenhoupt weights and maximal L
^{p}-regularity”.

Arch. Math. (Basel)**81**(2003), 422-430. - R. Haller, H. Heck, and A. Noll, “Mikhlin's theorem for operator-valued Fourier multipliers in n variables”.

Math. Nachr.**244**(2002), 110-130.

**Preprints and papers in preparation**

- S. Bechtel, R. M. Brown, R. Haller-Dintelmann, and P. Tolksdorf, “Extendability of functions with partially vanishing trace”.

Submitted.

arXiv:1910.06009 - R. Haller, H. Meinlschmidt, and J. Rehberg, “Hölder Regularity for Domains of Fractional Powers of Elliptic Operators with Mixed Boundary Conditions”.

Submitted.

arXiv:2210.03451

**PhD Thesis**

- R. Haller-Dintelmann, “Methoden der Banachraum-wertigen Analysis und Anwendungen auf parabolische Probleme” (Methods of the analysis of functions with values in Banach spaces and applications to parabolic problems).

Wissenschaftlicher Verlag Berlin, 2004.

**Habilitation**

- R. Haller-Dintelmann, “Lp-Regularity Theory for Linear Elliptic and Parabolic Equations”, habilitation thesis, TU Darmstadt, 2008.