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# Extension of some Lions-Magenes theorems

### Abstract

A general form of the Lions-Magenes theorems on solvability of an elliptic boundary-value problem in the spaces of nonregular distributions is proved. We find a general condition on the space of right-hand sides of the elliptic equation under which the operator of the problem is bounded and has a finite index on the corresponding couple of Hilbert spaces. Extensive classes of the spaces satisfying this condition are constructed. They contain the spaces used by Lions and Magenes and many others spaces.

### Article Information

 Title Extension of some Lions-Magenes theorems Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 2, 152-167 MathSciNet MR2553531 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

Aleksandr A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine; Chernigiv State Technological University, 95 Shevchenka, Chernigiv, 14027, Ukraine

### Citation Example

Aleksandr A. Murach, Extension of some Lions-Magenes theorems, Methods Funct. Anal. Topology 15 (2009), no. 2, 152-167.

### BibTex

@article {MFAT502,
AUTHOR = {Murach, Aleksandr A.},
TITLE = {Extension of some Lions-Magenes theorems},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {2},
PAGES = {152-167},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=502},
}