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

Anders Björn 1  and Daniel Hansevi 2
  • 1 Department of Mathematics, Linköping University, 581 83, Linköping, Sweden
  • 2 Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

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.

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Analysis and Geometry in Metric Spaces (AGMS) is a fully peer-reviewed, open access electronic journal that publishes cutting-edge original research on analytical and geometrical problems in metric spaces and their mathematical applications. It features articles making connections among relevant topics in this field.

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