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Transactions of the American Mathematical Society

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Analytic hypoellipticity of certain second-order evolution equations with double characteristics

Author: Mario Tosques
Journal: Trans. Amer. Math. Soc. 218 (1976), 173-196
MSC: Primary 35H05
MathSciNet review: 0402261
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Abstract: The present article establishes the analytic hypoellipticity (Definition 1.2) of a class of abstract evolution equations of order two, with double characteristics, under the hypothesis that the coefficients are analytic (in a suitable sense; see §2). The noteworthy feature of the main result (Theorem 4.1) is that analytic hypoellipticity holds whenever hypoellipticity does, even when one of the asymptotic eigenvalues $ {c^j}(A)$ fails to be elliptic of order one.

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Keywords: Evolution equation, hypoelliptic, analytic hypoelliptic, concatenation, scale of Hilbert spaces
Article copyright: © Copyright 1976 American Mathematical Society