scholarly journals Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces

2006 ◽  
Vol 58 (4) ◽  
pp. 1211-1232 ◽  
Author(s):  
Anders BJÖRN ◽  
Jana BJÖRN
Keyword(s):  
Harmonic Functions ◽  
Obstacle Problem ◽  
Metric Spaces ◽  
Boundary Regularity

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

2019 ◽  
Vol 7 (1) ◽  
pp. 179-196
Author(s):  
Anders Björn ◽  
Daniel Hansevi
Keyword(s):  
Harmonic Functions ◽  
Obstacle Problem ◽  
Metric Spaces ◽  
Local Property ◽  
Boundary Regularity ◽  
Obstacle Problems ◽  
Regular Boundary ◽  
Complete Metric Spaces ◽  
Regularity Results

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.

scholarly journals Harmonic functions on metric spaces

2001 ◽  
Vol 45 (3) ◽  
pp. 1021-1050 ◽  
Author(s):  
Nageswari Shanmugalingam
Keyword(s):  
Harmonic Functions ◽  
Metric Spaces

Fat sets and pointwise boundary estimates forp-harmonic functions in metric spaces

2001 ◽  
Vol 85 (1) ◽  
pp. 339-369 ◽  
Author(s):  
Jana Björn ◽  
Paul MacManus ◽  
Nageswari Shanmugalingam
Keyword(s):  
Harmonic Functions ◽  
Metric Spaces ◽  
Boundary Estimates

scholarly journals The Perron method for p-harmonic functions in metric spaces

2003 ◽  
Vol 195 (2) ◽  
pp. 398-429 ◽  
Author(s):  
Anders Björn ◽  
Jana Björn ◽  
Nageswari Shanmugalingam
Keyword(s):  
Harmonic Functions ◽  
Metric Spaces ◽  
Perron Method
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