Special Session 108: Regularity in local versus nonlocal problems

Unified regularity properties for minimizers under double-phase and exponential growth
Antonella Nastasi
University of Palermo
Italy
Co-Author(s):    Paolo Marcellini (University of Florence) and Cintia Pacchiano Camacho (Universidad Nacional Autonoma de Mexico)
Abstract:
In this talk we will present some general growth conditions for functionals, including the so-called natural growth, or polynomial, or growth conditions, or even exponential growth, in order to obtain that any local minimizer of the corresponding energy integral is locally Lipschitz continuous. In fact this is the fundamental step for further regularity; i.e., the general growth conditions a posteriori are reduced to a standard growth, with the possibility to apply the classical regularity theory. In other words, we reduce some classes of non-uniform elliptic variational problems to a context of uniform ellipticity. This is a joint work with Paolo Marcellini and Cintia Pacchiano Camacho.