Microlocal Cauchy problem for distribution solutions to systems with regular singularities

DOI10.1016/j.bulsci.2014.11.005zbMath1329.35024OpenAlexW2079639377MaRDI QIDQ496561

Susumu Yamazaki

Publication date: 22 September 2015

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2014.11.005

zbMATH Keywords

distributionmicrolocal analysis\(\mathcal{D}\)-modulesystems of analytic linear differential equations

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) Distributions and ultradistributions as boundary values of analytic functions (46F20) Initial value problems for systems of linear higher-order PDEs (35G40)

Cites Work

• dg-methods for microlocalization
• The Riemann-Hilbert problem for holonomic systems
• Semianalytic and subanalytic sets
• Cauchy problem for hyperbolic \(\mathcal{D}\)-modules with regular singularities
• Systems of differential equations with regular singularities and their boundary value problems
• Micro-hyperbolic systems
• Micro-support and Cauchy problem for temperate solutions of regular \({\mathcal D}\)-modules.
• On holonomic systems of microdifferential equations. III: Systems with regular singularities
• A generalization of Bochner's tube theorem in elliptic boundary value problems
• Higher-codimensional boundary value problems and \(F\)-mild microfunctions -- local and microlocal uniqueness --
• The correctness of the Cauchy problem
• Boundary values of hyperfunction solutions of linear partial differential equations
• Microlocalization of subanalytic sheaves
• Microlocalisation tempérée
• Moderate and formal cohomology associated with constructible sheaves
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