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

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We study <i>p</i>-harmonic functions in complete metric spaces equipped with a doubling Borel measure supporting a weak (1,<i>p</i>)-Poincaré inequality, 1<<i>p</i><∞. 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 <i>p</i>-harmonic functions and in the Euclidean setting to $¥mathscr{A}$-harmonic functions, with the usual assumptions on $¥mathscr{A}$.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(4), 1211-1232, 2006-10-01 

    The Mathematical Society of Japan

参考文献:  32件

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各種コード

  • NII論文ID(NAID)
    10018380957
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    8512899
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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