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On global hypoellipticity of degenerate elliptic operators

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Abstract.

We consider a class of degenerate elliptic operators on a torus and prove that global hypoellipticity is equivalent to an algebraic condition involving Liouville vectors and simultaneous approximability. For another class of operators we show that the zero order term may influence global hypoellipticity.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA (e-mail: alex.a.himonas.1@nd.edu) , , , , , , US

    A. Alexandrou Himonas & Gerson Petronilho

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  1. A. Alexandrou Himonas
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  2. Gerson Petronilho
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Received August 13, 1997

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Himonas, A., Petronilho, G. On global hypoellipticity of degenerate elliptic operators. Math Z 230, 241–257 (1999). https://doi.org/10.1007/PL00004693

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  • DOI: https://doi.org/10.1007/PL00004693

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