Double phase functionals with smooth weights

par Michal Borowski (University of Warsaw)

lundi 24 nov. 2025, 14:00 → 16:00 Europe/Paris

 I will discuss double phase functionals in the context of Lavrentiev’s phenomenon. Double phase functionals describe an energy that switches between two given power functions at different spatial points. The weight function controls this switch so that greater regularity implies a less abrupt switch.
Minimizing the functional over Lipschitz functions may result in a strictly greater value than over Sobolev functions. This produces Lavrentiev’s phenomenon and, further, the lack of regularity of minimizers. The greater the distance between exponents defining the power functions, the better the behavior is expected from the weight function. I will discuss how increasing the smoothness of the weight affects the range of exponents admissible for discarding Lavrentiev’s gap.
In the talk, I will further elaborate on the double phase functionals, the result, and its proof. The talk is based on the following preprint:
M. Borowski, Smoothness of weight sharply discards Lavrentiev’s gap for
double phase functionals, arXiv:2509.06567. (2025).