Lawruk elliptic boundaryvalue problems for homogeneous differential equations

TitleLawruk elliptic boundaryvalue problems for homogeneous differential equations
Publication TypeJournal Article
Year of Publication2019
AuthorsAnop, AV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published02/2019

We investigate Lawruk elliptic boundaryvalue problems for homogeneous differential equations in a twosided refined Sobolev scale. These problems contain additional unknown functions in the boundary conditions of arbitrary orders. The scale consists of innerproduct Hörmander spaces whose orders of regularity are given by any real number and a function which varies slowly at infinity in the sense of Karamata. We establish theorems on the Fredholm property for the problems in the refined Sobolev scale and on local regularity and local a priori estimate (up to the boundary of the domain) of their generalized solutions. We find sufficient conditions under which components of these solutions are functions continuously differentiable l > …0 times.

Keywordsa priori estimate, elliptic boundaryvalue problem, Fredholm operator, refined Sobolev scale, regularity of solution

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