Open Access

Parameter-elliptic operators on the extended Sobolev scale

     Article (.pdf)

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 a Hilbert-Sobolev scale. We prove that these operators set isomorphisms between appropriate spaces of the scale provided the absolute value of the parameter is 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.

Key words: Parameter–elliptic operator, extended Sobolev scale, H¨ormander space, ROvarying function, interpolation with function parameter, isomorphism property, a priory estimate of solutions.


Full Text





Article Information

TitleParameter-elliptic operators on the extended Sobolev scale
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 29-39
MathSciNet MR3088076
zbMATH 1289.58011
MilestonesReceived 03/12/2012
CopyrightThe Author(s) 2013 (CC BY-SA)

Authors Information

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Tetiana Zinchenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine


Citation Example

Aleksandr A. Murach and Tetiana Zinchenko, Parameter-elliptic operators on the extended Sobolev scale, Methods Funct. Anal. Topology 19 (2013), no. 1, 29-39.


BibTex

@article {MFAT676,
    AUTHOR = {Murach, Aleksandr A. and Zinchenko, Tetiana},
     TITLE = {Parameter-elliptic operators on the extended Sobolev scale},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {29-39},
      ISSN = {1029-3531},
  MRNUMBER = {MR3088076},
 ZBLNUMBER = {1289.58011},
       URL = {http://mfat.imath.kiev.ua/article/?id=676},
}


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar


Export article

Save to Mendeley


All Issues