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

• Akamatsu Toyohiro

  Department of Mathematics, Tokai University

Abstract

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(x) and the sum of squares of first order operators X₁,…,X_r. These conditions are related to the way in which φ(x) changes its sign, and the rank of the Lie algebra generated by φX₁,…,φX_r and X₀ where X₀ is the first order term of the operator. Our result is an extension of that of [4], and it includes some cases not treated in [1], [5] and [8].

Journal

• Journal of the Mathematical Society of Japan

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

  The Mathematical Society of Japan

Keywords

• second order operator
• hypoellipticity
• estimate of the subelliptic kind

Details

• CRID: 1390001205116588544
• NII Article ID: 10018380803
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/1179759537
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2276181
• NDL BIB ID: 8512843
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8512843
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed