Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces

Abstract

The theory of boundary regularity for p-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.

Keywords

• barrier
• boundary regularity
• kellogg property
• metric space
• obstacle problem
• p-harmonic function
• primary: 31e05
• secondary: 30l99, 35j66, 35j92, 49q20