Minimal normalization of mixed boundary value problems
by
Frank-Olme Speck
Universidade Technica de Lisboa, Departamento de Matematica, 1049-001 Lisboa, Portugal

A class of mixed boundary value problems (BVPs) is considered in spaces of Bessel potentials. By localization, an operator L associated with the BVP is reduced to a family of pseudo-differential operators which leads to a Fredholm criterion for L. But particular attention is devoted to the non-Fredholm case where the image of L is not closed. Minimal normalization, which means a certain minimal change of the spaces under consideration such that the continuous extension of L or the image restriction is normally solvable, leads to modified spaces of Bessel potentials. These are characterized in a physically relevant sense and seen to be very much related to operators with transmission property (domain normalization) or to problems with compatibility conditions for the data (image normalization), respectively.

Date received: May 31, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahs-57.