Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces

Abstract

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.

Full Text

Article Information

Title	Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces
Source	Methods Funct. Anal. Topology, Vol. 21 (2015), no. 1, 6-21
MathSciNet	3407917
zbMATH	06533464
Milestones	Received 25/11/2014
Copyright	The Author(s) 2015 (CC BY-SA)

Authors Information

I. S. Chepurukhina
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

A. A. Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 25/11/2014

Citation Example

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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