Speaker
Antonella Nastasi, University of Palermo
Abstract
The talk shall focus on a class of double phase integrals characterized by nonstandard growth conditions, which constitute an important sub-field of the calculus of variations. Variational methods are powerful tools in investigating the behaviour and regularity properties of minimizers and, more generally, quasiminimizers that minimize the energy integral up to a multiplicative constant. We study regularity theory, specifically local and global higher integrability, for quasiminimizers of a double phase integral with $(p, q)$-growth. The proofs follow a variational approach in the setting of metric measure spaces with a doubling measure and a Poincaré inequality. The main feature of the study is an intrinsic approach to double phase Sobolev-Poincaré inequalities. The results are part of a joint paper with Juha Kinnunen (Aalto University) and Cintia Pacchiano Camacho (Calgary University).