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# Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces

### Abstract

We investigate a general nonhomogeneous initial-boundary value problem for a two-dimensional parabolic equation in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hörmander spaces.

Key words: Parabolic initial-boundary value problem, Hörmander space, slowly varying function, isomorphism property, interpolation with a function parameter.

### Article Information

 Title Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 2, 177-191 MathSciNet MR3668813 zbMATH 06810676 Milestones Received 07/03/2017 Copyright The Author(s) 2017 (CC BY-SA)

### Authors Information

Valerii Los
National Technical University of Ukraine ”Igor Sikorsky Kyiv Polytechnic Institute”, 37 Prospect Peremohy, Kyiv, 03056, Ukraine

### Citation Example

Valerii Los, Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces, Methods Funct. Anal. Topology 23 (2017), no. 2, 177-191.

### BibTex

@article {MFAT971,
AUTHOR = {Valerii Los},
TITLE = {Initial-boundary value problems for two-dimensional
parabolic equations in Hörmander spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {2},
PAGES = {177-191},
ISSN = {1029-3531},
MRNUMBER = {MR3668813},
ZBLNUMBER = {06810676},
URL = {http://mfat.imath.kiev.ua/article/?id=971},
}

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