Boundary Regularity for p-Harmonic Functions and Solutions of Obstacle Problems on Unbounded Sets in Metric Spaces
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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.
2006 ◽
Vol 58
(4)
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pp. 1211-1232
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2015 ◽
Vol 373
(2050)
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pp. 20140449
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2001 ◽
Vol 37
(1-2)
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pp. 169-184
2018 ◽
Vol 6
(8)
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pp. 297