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# Elliptic problems with unknowns on the boundary and irregular boundary data

### Abstract

We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically, irregular) distributions. We investigate local (up to the boundary) properties of generalized solutions to the problem in Hilbert distribution spaces that belong to the refined Sobolev scale. These spaces are parametrized with a real number and a function that varies slowly at infinity. The function parameter refines the number order of the space. We prove theorems on local regularity and a local a priori estimate of generalized solutions to the problem under investigation. These theorems are new for Sobolev spaces as well.

Key words: Elliptic problem, refined Sobolev scale, Fredholm operator, boundary data, generalized solution, a priori estimate, regularity of solution.

### Article Information

 Title Elliptic problems with unknowns on the boundary and irregular boundary data Source Methods Funct. Anal. Topology, Vol. 26 (2020), no. 2, 91-102 DOI 10.31392/MFAT-npu26_2.2020.01 MathSciNet MR4127606 Milestones Received 11.06.2020 Copyright The Author(s) 2020 (CC BY-SA)

### Authors Information

Iryna Chepurukhina
Institute of Mathematics of the National Academy of Sciences of Ukraine, Tereshchenkivs’ka 3, Kyiv 01024, Ukraine

Aleksandr Murach
Institute of Mathematics of the National Academy of Sciences of Ukraine, Tereshchenkivs’ka 3, Kyiv 01024, Ukraine

### Citation Example

Iryna Chepurukhina and Aleksandr Murach, Elliptic problems with unknowns on the boundary and irregular boundary data, Methods Funct. Anal. Topology 26 (2020), no. 2, 91-102.

### BibTex

@article {MFAT1340,
AUTHOR = {Iryna Chepurukhina and Aleksandr Murach},
TITLE = {Elliptic problems with unknowns on the boundary and irregular boundary data},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {2},
PAGES = {91-102},
ISSN = {1029-3531},
MRNUMBER = {MR4127606},
DOI = {10.31392/MFAT-npu26_2.2020.01},
URL = {http://mfat.imath.kiev.ua/article/?id=1340},
}

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