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

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概要

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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(x) and the sum of squares of first order operators X1,…,Xr. These conditions are related to the way in which φ(x) changes its sign, and the rank of the Lie algebra generated by φX1,…,φXr 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].

• 社団法人 日本数学会の論文
• 2006-10-01

著者

• AKAMATSU Toyohiro

  Department of Mathematics Faculty of Science Osaka University

• Akamatsu Toyohiro

  Department Of Mathematics Tokai University

関連論文

• On a parametrix in some weak sense of a first order linear partial differential operator with two independent variables
• On Necessary Condition (P) of F. Treves for Hypoellipticity of Linear Partial Differential Operator of Principal Type
• Hypoellipticity of Some Degenerate Parabolic Operators
• Remarks on ranks of Lie algebras associated with a second order partial differential operator and necessary conditions for hypoellipticity
• Remarks on the Rank of a Lie Algebra and Necessary Conditions for Hypoellipticity of a Degenerate Parabolic Operator
• Hypoellipticity of a second order operator with a principal symbol changing sign across a smooth hypersurface

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