Boundary regularity for quasiminima of double-phase problems on metric spaces
Analysis of PDEs
2025-07-25 v4 Metric Geometry
Abstract
We give a sufficient condition for H\"older continuity at a boundary point for quasiminima of double-phase functionals of -Laplace type, in the setting of metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality. We use a variational approach based on De Giorgi-type conditions to give a pointwise estimate near a boundary point. The proofs are based on a careful phase analysis and estimates in the intrinsic geometries.
Keywords
Cite
@article{arxiv.2412.04978,
title = {Boundary regularity for quasiminima of double-phase problems on metric spaces},
author = {Antonella Nastasi and Cintia Pacchiano Camacho},
journal= {arXiv preprint arXiv:2412.04978},
year = {2025}
}