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- W150652989 abstract "Publisher SummaryThis chapter presents some applications of microlocal energy methods to analytic hypoellipticity. The chapter extends the “microlocal energy methods” in microfunction theory to system-cases admitting some degeneracy. New proofs of analytic hypoellipticity for parabolic boundary value problems, and for Treves-type operators with double characteristics are presented. The chapter also discusses some new results for more degenerate operators. The theorem that “quasi-positivity” also gives an order structure to Hermite microkernels at p0, which is weaker than “≪”, is also proven. The analyticity of solutions for parabolic boundary value problems can be proven by constructing fundamental solutions with estimates for analytic wave front sets. For example, if the coefficients do not depend on the time variable, the theory of analytic semi-groups will be applicable. Various propositions are also presented in the chapter." @default.
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- W150652989 date "1988-01-01" @default.
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- W150652989 title "Some Applications of Microlocal Energy Methods to Analytic Hypoellipticity" @default.
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- W150652989 doi "https://doi.org/10.1016/b978-0-12-400465-8.50031-6" @default.
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