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“He who seeks for methods without having a definite problem in mind seeks for the most part in vain.”

David Hilbert

Webpage last updated March 6, 2021

  • Stochastic partial differential equations
  • (Stochastic) variational calculus
  • Singular and degenerate stochastic diffusion equations in Hilbert space
  • Nonlocal and local nonlinear stochastic evolution equations
  • Linear growth functionals and variational convergence
  • Ergodic theory and invariant distributions
  • Dirichlet forms and their geometry
  • Models from biology, ecology and neuroscience

Submitted for peer review

  • J. M. Tölle (with F. Seib and W. Stannat). Stability and moment estimates for the stochastic singular Φ-Laplace equation. Preprint, submitted (2021), 23 pp., arXiv:2103.03194.

    Abstract.

  • J. M. Tölle (with E. Hausenblas). The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. Preprint, submitted (2021), 52 pp., arXiv:1912.00996.

    Abstract.

  • J. M. Tölle (with M. Hinz and L. Viitasaari). Variability of paths and differential equations with BV-coefficients. Preprint, submitted (2020), 68 pp., arXiv:2003.11698.

    Abstract.

Journal Publications

Published in peer reviewed proceedings

      1. J. M. Tölle. Estimates for nonlinear stochastic partial differential equations with gradient noise via Dirichlet forms. In: Eberle A., Grothaus M., Hoh W., Kassmann M., Stannat W., Trutnau G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_14.

Other works

      1. J. M. Tölle (with P. Beissner). A compact topology for σ-algebra convergence. Working paper, (2018), 23 pp., arXiv:1802.05920.
      2. J. M. Tölle. Convergence of solutions to the p-Laplace evolution equation as p goes to 1. Preprint, http://arxiv.org/abs/1103.0229v2, 2011, 11 pp.

Theses

      1. J. M. Tölle. Stochastic partial differential equations with singular drift. Habilitation thesis, Universität Augsburg, 2019, 232 pp.
      2. J. M. Tölle. Variational convergence of nonlinear partial differential operators on varying Banach spaces. Dissertation, Universität Bielefeld, published online on BieSOn, Universitätsbibliothek Bielefeld, urn:nbn:de:hbz:361-16758, 2010, 250 pp, pdf.
      3. J. M. Tölle. Convergence of non-symmetric forms with changing reference measures. Diploma thesis, Universität Bielefeld, BiBoS-Preprint E06-09-234, http://www.math.uni-bielefeld.de/~bibos/preprints/E06-09-234.pdf, 2006, 81 pp.

(in chronological order – most recent first)

Erdős number: 3
P. Erdős — C. J. Colbourn — M. Scheutzow — J. M. Tölle