Micro-local theory of boundary value problems I : Theory of mild hyperfunctions and Green's formula
Kiyômi Kataoka · Institutional Repositories DataBase (IRDB) · 1980
In [9] and [11], H. Komatsu-T. Kawai and P. Schapira defined boundary values of hyperfunction solutions to non-characteristic boundary value problems. Since then, many works have been published. Above all the Green formula used by A. Kaneko seems to be very fundamental for boundary value problems. The author introduces the concept of mildness for hyperfunctions, which expresses a wide class of hyperfunctions having boundary values, and shows that mildness is kept under several operations : integration along fiber, product, ･･･, and so on. Simultaneously mildness and these operations are micro-localized and the relationship with boundary value problems for pseudo-differential operators is clarified. The Green formula, in particular, is also micro-localized, too. Lastly the consistency with topological boundary values is stated.