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

2024/12/06 by Nastasi, Antonella, Camacho, Cintia Pacchiano
#31C45 #35J60 #46E35 #49N60 #49Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi: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.

Related

• Regularity results for quasiminima of a class of double phase problems
• Gradient higher integrability for double phase problems on metric measure spaces
• Regularity of sets with quasiminimal boundary surfaces in metric spaces
• Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data
• Hölder regularity for degenerate parabolic double-phase equations