Year: 2012
Type: preprint
Abstract: Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. We prove that these operators set isomorphisms between appropriate spaces of the scale provided the parameter is modulo large enough. For solutions to the corresponding parameter--elliptic equations, we establish two-sided a priori estimates, in which the constants are independent of the parameter.
Source: arXiv (Cornell University)
Authors: Murach, Aleksandr A., Zinchenko, Tetiana
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2487679330