I. S. Chepurukhina

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Articles: 1

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

Iryna S. Chepurukhina, Aleksandr A. Murach

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 1, 6-21

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.

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