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# Elliptic boundary-value problems in Hörmander spaces

### Abstract

We investigate general elliptic boundary-value problems in Hörmander inner product spaces that form the extended Sobolev scale. The latter consists of all Hilbert spaces that are interpolation spaces with respect to the Sobolev Hilbert scale. We prove that the operator corresponding to an arbitrary elliptic problem is Fredholm in appropriate couples of the Hörmander spaces and induces a collection of isomorphisms on the extended Sobolev scale. We obtain a local a priory estimate for generalized solutions to this problem and prove a theorem on their local regularity in the Hörmander spaces. We find new sufficient conditions under which generalized derivatives (of a given order) of the solutions are continuous.

Key words: Elliptic problem, Hörmander space, extended Sobolev scale, RO-varying function, Fredholm property, a priori estimate, local regularity

### Article Information

 Title Elliptic boundary-value problems in Hörmander spaces Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 4, 295-310 MathSciNet MR3591082 zbMATH 06742113 Milestones Received 19/09/2016 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

Anna Anop
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine; Chernihiv National Pedagogical University, 53 Het’mana Polubotka, Chernihiv, 14013, Ukraine

Tetiana Kasirenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

### Citation Example

Anna Anop and Tetiana Kasirenko, Elliptic boundary-value problems in Hörmander spaces, Methods Funct. Anal. Topology 22 (2016), no. 4, 295-310.

### BibTex

@article {MFAT911,
AUTHOR = {Anop, Anna and Kasirenko, Tetiana},
TITLE = {Elliptic boundary-value problems in Hörmander spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {4},
PAGES = {295-310},
ISSN = {1029-3531},
MRNUMBER = {MR3591082},
ZBLNUMBER = {06742113},
URL = {http://mfat.imath.kiev.ua/article/?id=911},
}

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