Analytic hypoellipticity of certain second-order evolution equations with double characteristics
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- by Mario Tosques PDF
- Trans. Amer. Math. Soc. 218 (1976), 173-196 Request permission
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.References
- François Trèves, Concatenations of second-order evolution equations applied to local solvability and hypoellipticity, Comm. Pure Appl. Math. 26 (1973), 201–250. MR 340804, DOI 10.1002/cpa.3160260206
- V. V. Grušin, A certain class of elliptic pseudodifferential operators that are degenerate on a submanifold, Mat. Sb. (N.S.) 84 (126) (1971), 163–195 (Russian). MR 0283630 F. Trèves, Ovcyannicov theorem and hyperdifferential operators, Notas de Matemática, no. 46, Instituto de Matematica Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968. MR 44 #7386.
- Louis Boutet de Monvel and François Trèves, On a class of pseudodifferential operators with double characteristics, Invent. Math. 24 (1974), 1–34. MR 353064, DOI 10.1007/BF01418785
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 218 (1976), 173-196
- MSC: Primary 35H05
- DOI: https://doi.org/10.1090/S0002-9947-1976-0402261-2
- MathSciNet review: 0402261