Robert Haller

• 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.