Lawruk elliptic boundaryvalue problems for homogeneous differential equations

1Anop, AV
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 2:3-11
Section: Mathematics
Language: Ukrainian

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.

Keywords: a priori estimate, elliptic boundaryvalue problem, Fredholm operator, refined Sobolev scale, regularity of solution

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