We investigate elliptic boundary-value problems with additional unknown functions on the boundary of a Euclidean domain. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on two-sided refined scales built on the base of inner product isotropic H\"ormander spaces. The regularity of the distributions forming these spaces are characterized by a real number and an arbitrary function that varies slowly at infinity in the sense of Karamata. For the generalized solutions to the problem, we prove theorems on a priori estimates and local regularity in these scales. As applications, we find new sufficient conditions under which the solutions have continuous classical derivatives of a prescribed order.
Key words: Elliptic boundary-value problem, slowly varying function, H¨ormander space, two-sided refined scale, Fredholm operator, a priori estimate for solutions, local regularity of solutions.
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Title
Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces
Iryna S. Chepurukhina and Aleksandr A. Murach, Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces, Methods Funct. Anal. Topology 21
(2015), no. 1, 6-21.
BibTex
@article {MFAT765,
AUTHOR = {Chepurukhina, Iryna S. and Murach, Aleksandr A.},
TITLE = {Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {1},
PAGES = {6-21},
ISSN = {1029-3531},
MRNUMBER = {3407917},
ZBLNUMBER = {06533464},
URL = {http://mfat.imath.kiev.ua/article/?id=765},
}
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