Extension theorems for the distribution solutions to $\mathcal {D}$-modules with regular singularities

Moduli of regular holonomic D-modules with normal crossing singularities

This paper solves the global moduli problem for regular holonomic Dmodules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to “pre-D-modules”), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-D-modules. A...

Moduli of Regular Holonomic -modules with Normal Crossing Singularities

Micro-support and Cauchy Problem for Temperate Solutions of Regular D-modules

Let X be a complex manifold, V a smooth involutive submanifold of T X, M a microdifferential system regular along V , and F an R-constructible sheaf on X. We study the complex of temperate microfunction solutions of M associated with F , that is, the complex RHomDX (M, T μhom(F,OX)). We give a bound to its micro-support and solve the Cauchy problem under a suitable hyperbolicity assumption.

Microsupport of Whitney Solutions to Systems with Regular Singularities and Its Applications

For systems of holomorphic linear differential equation with regular singularities in the sense of Kashiwara-Oshima, it is obtained that the bound to microsupport of the solution complex of the formal cohomology associated with constructible sheaf due to Kashiwara-Schapira. As applications, hyperbolic Cauchy and boundary value problems are considered for Whitney functions.

Extension theorems for plate elements with applications

Extension theorems for plate elements are established. Their applications to the analysis of nonoverlapping domain decomposition methods for solving the plate bending problems are presented. Numerical results support our theory.