دانلود کتاب Non-Homogeneous Boundary Value Problems and Applications: Vol. 3

1. Our essential objective is the study of the linear, non-homogeneous
problems:
(1) Pu == f in (9, an open set in R N ,
(2) fQjU == gj on 8(9 (boundp,ry of (f)),
lor on a subset of the boundary 8(9 1 < i < v,
where P is a linear differential operator in (9 and where the Q/s are linear
differen tial operators on 8(f).
In Volumes 1 and 2, we studied, for particular classes of systems
{P, Qj}, problem (1), (2) in classes of Sobolev spaces (in general constructed
starting from L2) of positive integer or (by interpolation) non-integer
order; then, by transposition, in classes of Sobolev spaces of negative
order, until, by passage to the limit on the order, we reached the spaces
of distributions of finite order.
In this volume, we study the analogous problems in spaces of infinitely
differentiable or analytic functions or of Gevrey-type functions and by
duality, in spaces of distributions, of analytic functionals or of Gevrey-
type ultra-distributions. In this manner, we obtain a clear vision (at least
we hope so) of the various possible formulations of the boundary value
problems (1), (2) for the systems {P, Qj} considered here.