Theoretical analysis demonstrates boundary Hölder continuity for double-phase quasiminima in doubling metric measure spaces, highlighting intrinsic geometric estimates.
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.
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Nastasi et al. (2026) studied this question.
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