Submitted Paper

Inserted: 9 dec 2024

Year: 2024
Doi: https://doi.org/10.48550/arXiv.2412.04978

Abstract:

We give a sufficient condition for Hölder continuity at a boundary point for quasiminima of double-phase functionals of p,q-Laplace type, in the setting of metric measure spaces equipped with a doubling measure and supporting a Poincaré 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.