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arXiv · 2412.04978

Boundary regularity for quasiminima of double-phase problems on metric spaces

Antonella Nastasi·Cintia Pacchiano Camacho
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Abstract

We give a sufficient condition for H\"older 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 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.

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Antonella Nastasi, Cintia Pacchiano Camacho. 2024-12-06. Boundary regularity for quasiminima of double-phase problems on metric spaces. https://arxiv.org/abs/2412.04978

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