Extension theory for elliptic partial differential operators with pseudodifferential methods
Analysis of PDEs
2014-11-04 v3 Spectral Theory
Abstract
This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very useful here, not only as a formulational framework, but also for the solution of specific questions. We recall some elements of that theory, and show its application in several cases (including recent results), namely to the lower boundedness question, and the question of spectral asymptotics for differences between resolvents.
Cite
@article{arxiv.1008.1081,
title = {Extension theory for elliptic partial differential operators with pseudodifferential methods},
author = {Gerd Grubb},
journal= {arXiv preprint arXiv:1008.1081},
year = {2014}
}
Comments
26 pages, style changed to LaTeX, new material added at the end, to appear in the Lecture Notes Series of the London Math. Soc. published by Cambridge Univ. Press