Vectorial Double Phase Obstacle Problems

TL;DR

This paper studies the regularity of vector-valued solutions that minimize certain double phase functionals with obstacle constraints, focusing on their partial smoothness properties.

Contribution

It introduces new partial regularity results for vector-valued minimizers under obstacle constraints with specific topological conditions.

Findings

Establishment of partial regularity for minimizers

Identification of conditions ensuring regularity near obstacles

Extension of regularity theory to vector-valued double phase problems

Abstract

We investigate partial regularity for vector valued local minimizers of double phase functionals, under vectorial obstacle type constraints satisfying appropriate topological properties.