Hypoellipticity of a second order operator with a principal symbol changing sign across a smooth hypersurface

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We give sufficient conditions for hypoellipticity of a second order operator with real-valued infinitely differentiable coefficients whose principal part is the product of a real-valued infinitely differentiable function φ(<i>x</i>) and the sum of squares of first order operators <i>X</i><sub>1</sub>,…,<i>X</i><sub><i>r</i></sub>. These conditions are related to the way in which φ(<i>x</i>) changes its sign, and the rank of the Lie algebra generated by φ<i>X</i><sub>1</sub>,…,φ<i>X</i><sub><i>r</i></sub> and <i>X</i><sub>0</sub> where <i>X</i><sub>0</sub> is the first order term of the operator. Our result is an extension of that of [<b>4</b>], and it includes some cases not treated in [<b>1</b>], [<b>5</b>] and [<b>8</b>].

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(4), 1037-1077, 2006-10-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10018380803
  • 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
    8512843
  • 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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