Micro-support and Cauchy problem for temperate solutions of regular \({\mathcal D}\)-modules.

zbMATH Open1038.35006arXivmath/0012088MaRDI QIDQ1406600

Masaki Kashiwara, Teresa Monteiro Fernandes, Pierre Schapira

Publication date: 2001

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Abstract: Let $X$ be a complex manifold, $V$ a smooth involutive submanifold of $T^{*}X$, $calM$ a microdifferential system regular along $V$, and $F$ an $mathbbR$-constructible sheaf on $X$. The complex of temperate microfunction solutions of $calM$ associated with $F$ is now well understood. In this paper we study the temperate case and give a bound to the micro-support of the temperate microfunction solution sheaves and solve the Cauchy problem under suitable hyperbolicity conditions.

Full work available at URL: https://arxiv.org/abs/math/0012088

zbMATH Keywords

Cauchy problemtemperate microfunction solutions

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Differential complexes (58J10)

Related Items (3)

Microlocal Cauchy problem for distribution solutions to systems with regular singularities ⋮ Functorial properties of the microsupport and regularity for ind-sheaves ⋮ Multi-microlocalization and microsupport

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