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Boundary regularity for <i>p</i>-harmonic functions and solutions of the obstacle problem on metric spaces
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- Björn Anders
- Department of Mathematics, Linköpings universitet
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- Björn Jana
- Department of Mathematics, Linköpings universitet
Bibliographic Information
- Other Title
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- Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces
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Description
We study p-harmonic functions in complete metric spaces equipped with a doubling Borel measure supporting a weak (1,p)-Poincaré inequality, 1<p<∞. We establish the barrier classification of regular boundary points from which it also follows that regularity is a local property of the boundary. We also prove boundary regularity at the fixed (given) boundary for solutions of the one-sided obstacle problem on bounded open sets. Regularity is further characterized in several other ways. <br>Our results apply also to Cheeger p-harmonic functions and in the Euclidean setting to $¥mathscr{A}$-harmonic functions, with the usual assumptions on $¥mathscr{A}$.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 58 (4), 1211-1232, 2006
The Mathematical Society of Japan
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Keywords
Details 詳細情報について
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- CRID
- 1390282680093311232
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- NII Article ID
- 10018380957
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- MRID
- 2276190
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- NDL BIB ID
- 8512899
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL Search
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed