15:00 - 16:00
Cristiana de Filippis
Lectures, talks and seminars
Mathematical Sciences, Department of
Jesus Martinez-Garcia email@example.com
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.
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  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].
Cristiana de Filippis, University of Oxford
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 firstname.lastname@example.org.