Higher-Codimensional Boundary Value Problems and <I>F</I>-Mild Microfunetions —Local and Microlocal Uniqueness—

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  • Oaku Toshinori
    Department of Mathematical Sciences, Yokohama City University
  • Yamazaki Susumu
    Research Fellow of The Japan Society for The Promotion of Science, Graduate School of Mathematical Sciences, The University of Tokyo

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  • Higher-Codimensional Boundary Value Problems and $F$-Mild Microfunctions —Local and Microlocal Uniqueness—
  • Higher-codimensional boundary value problems and F-mild microfunctions

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For the study of local and microlocal boundary value problems with a boundary of codimension greater than one, sheaves of F-mild hyperfunctions and F-mild microfunctions are introduced. They are refinements of the notions of hyperfunctions and microfunctions with real analytic parameters and have natural boundary values. F-mild solutions of a general \mathscr{D}-Module \mathscr{M} (that is, a system of linear partial differential equations with analytic coefficients) are considered. In particular, local and microlocal uniqueness in the boundary value problem (the Holmgren type theorem) is proved if the boundary is non-characteristic for \mathscr{M}. or else if \mathscr{M} is Fuchsian along the boundary.

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