Extension of some Lions-Magenes theorems

Details Extension of some Lions-Magenes theorems Extension of some Lions-Magenes theorems

2009-03-31

arxiv.org/abs/0903.5421v1

Methods Funct. Anal. Topology, 15 (2009), no. 2, 152--167.

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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.

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