Interpolation between Subspaces of Hilbert Spaces
and Applications to Shift Theorems for Elliptic Boundary Value Problems
Abstract:
In the real method of interpolation one starts with two Hilbert spaces,
$X$ and $Y$, with certain properties and constructs a family of Hilbert
spaces called the interpolation spaces. In applications to partial
differential equations and finite element methods, the following question
often arises: If the interpolation spaces $X$ and $Y$ are known Sobolev
spaces, and if $X_M$ and $Y_N$ are closed subspaces of $X$ and $Y$,
respectively, what are the interpolation spaces of
$X_M$ and $Y_N$ ? For certain boundary value problems, the answer to this
kind of question, together with a complete characterization of the range
of the corresponding differential operator, leads to stability estimates
for solutions in terms of fractional norms. These types of estimates are
known as shift theorems.
Some new interpolation results
and shift theorems for the special case of polygonal domains are
presented.
Converted from bacuta.txt (plain text).