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Research

Home Research

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

Scientific Interests

  • stochastic partial differential equations
  • (stochastic) variational calculus
  • singular and degenerate stochastic diffusion equations in Hilbert space
  • nonlocal and local nonlinear stochastic partial differential equations
  • linear growth functionals and variational convergence
  • ergodic theory and invariant distributions
  • Dirichlet forms and their geometry
  • Sobolev space theory

Links

Google Scholar, arXiv, Orcid, ResearcherID.

List of Publications

for Jonas M. Tölle

updated July 24, 2018
Erdős number: 3
P. Erdős — C. J. Colbourn — M. Scheutzow — J. M. Tölle

Submitted for peer review

  1. J. M. Tölle (with C. Kuehn). A gradient flow formulation for the stochastic Amari neural field model. Preprint, submitted (2018), 18 p, arXiv:1807.02575.

    Abstract.

  2. J. M. Tölle. Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions. Preprint, submitted (2018), 25 pp., arXiv:1803.07005.

    Abstract.

  3. J. M. Tölle (with P. Beissner). A compact topology for σ-algebra convergence. Preprint, submitted (2017), 23 pp., arXiv:1802.05920.

    Abstract.

Journal Publications

  1. J. M. Tölle (with B. Gess). Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations. SIAM J. Math. Anal. 48 (2016), no. 6, 4094–4125, http://dx.doi.org/10.1137/15M1049774, preprint available at arXiv:1507.04545.
  2. J. M. Tölle (with I. Ciotir). Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise. J. Funct. Anal. 271 (2016), no. 7, 1764–1792, http://dx.doi.org/10.1016/j.jfa.2016.05.013, preprint available at arXiv:1507.02576.
  3. J. M. Tölle (with B. Gess). Stability of solutions to stochastic partial differential equations. J. Differential Equations 260 (2016), no. 6, 4973–5025, http://dx.doi.org/10.1016/j.jde.2015.11.039, preprint available at arXiv:1506.01230.
  4. J. M. Tölle (with B. Gess). Multi-valued, singular stochastic evolution inclusions. J. Math. Pures Appl. 101 (2014), no. 6, 789–827, http://dx.doi.org/10.1016/j.matpur.2013.10.004, preprint available at arXiv:1112.5672.
  5. J. M. Tölle (with A. Es-Sarhir, M. Scheutzow and O. van Gaans). Invariant measures for monotone SPDEs with multiplicative noise term. Appl. Math. Optim. 68 (2013), no. 2, 275–287, http://dx.doi.org/10.1007/s00245-013-9206-4, preprint available at arXiv:0910.0960.
  6. J. M. Tölle (with I. Ciotir). Corrigendum to “Convergence of invariant measures for singular stochastic diffusion equations” [Stochastic Process. Appl. 122 (2012) 1998–2017.] Stochastic Process. Appl. 123 (2013), no. 3, 1178–1181, http://dx.doi.org/10.1016/j.spa.2012.10.009, preprint available at arXiv:1211.4404.
  7. J. M. Tölle. Uniqueness of weighted Sobolev spaces with weakly differentiable weights. J. Funct. Anal. 263 (2012), no. 10, 3195–3223, http://dx.doi.org/10.1016/j.jfa.2012.08.002, preprint available at arXiv:1110.2888.
  8. J. M. Tölle (with I. Ciotir). Convergence of invariant measures for singular stochastic diffusion equations. Stochastic Process. Appl. 122 (2012), no. 4, 1998–2017, http://dx.doi.org/10.1016/j.spa.2011.11.011, preprint available at arXiv:1201.2839.
  9. J. M. Tölle (with M.-K. von Renesse). On an EVI curve characterization of Hilbert spaces. J. Math. Anal. Appl. 385 (2012), 589–598, http://dx.doi.org/10.1016/j.jmaa.2011.06.080.
  10. J. M. Tölle (with W. Liu). Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts. Electr. Comm. Probab. 16 (2011), 447–457, http://ecp.ejpecp.org/article/view/1643, preprint available at arXiv:1109.2437.

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 (online)

  1. 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.
  2. J. M. Tölle (with I. Ciotir). Convergence of solutions to the stochastic p-Laplace equation as p goes to 1. BiBoS Preprint 11-01-371, SFB 701 Preprint 11002. http://www.math.uni-bielefeld.de/~bibos/preprints/11-01-371.pdf, 2010, 16 pp.
  3. J. M. Tölle. Revision of Variational convergence of nonlinear partial differential operators on varying Banach spaces. http://www.math.uni-bielefeld.de/~bibos/preprints/E10-09-360.pdf, 2010, 250 pp.
  4. 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): urn:nbn:de:hbz:361-16758, 2010, 250 pp.
  5. 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.