Differentiable vs non-differentiable systems

  • Thu 25 Feb 21

    15:00 - 16:00

  • Online


  • Event speaker

    Cristiana de Filippis

  • Event type

    Lectures, talks and seminars

  • Event organiser

    Mathematical Sciences, Department of

  • Contact details

    Jesus Martinez-Garcia

These Departmental Seminars are for everyone in Maths. We encourage anyone interested in the subject in general, or in the particular subject of the seminar, to come along. It's a great opportunity to meet people in the Maths Department and join in with our community.

Differentiable vs non-differentiable systems

Nonautonomous, nonuniformly elliptic functionals are variational integrals characterised by quite a wild behaviour of the ellipticity ratio associated to their integrand, in the sense that it may blow up as the modulus of the gradient variable goes to infinity.

We analyse the interaction between the space-depending coefficient of the integrand and a possible forcing term and derive optimal Lipschitz criteria for minimizers. We catch the main model cases appearing in the literature, such as functionals with unbalanced power growth or with fast exponential growth. We also find new borderline regularity results also in the uniformly elliptic case, i.e. when the ellipyicity ratio is uniformly bounded.

This approach yields optimal regularity results for obstacle problems associated for instance to iterated exponential models, which have been treated in [2] for the first time. Finally, we look at general nonautonomous integrands with (p,q)-growth and show general interpolation properties allowing to get basic higher integrability results for either bounded or Hölder continuous minimizers under improved bounds for the gap q-p.

This talk is based on papers [1,2,3].


  • [1] C. De Filippis, G. Mingione, Interpolative gap bounds for nonautonomous integrals. Preprint (2020), submitted.
  • [2] C. De Filippis, G. Mingione, Lipschitz bounds and nonautonomous integrals. Preprint (2020), submitted. https://arxiv.org/pdf/2007.07469.pdf
  • [3] C. De Filippis, G. Mingione, On the regularity of minima of non-autonomous functionals. Journal of Geometric Analysis 30:1584-1626, (2020). https://doi.org/10.1007/s12220-019-00225-z


Cristiana de Filippis, University of Oxford

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia jesus.martinez-garcia@essex.ac.uk.

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