Related papers: Elliptic operators on refined Sobolev scales on ve…
In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the…
We study an extended Sobolev scale for smooth vector bundles over a smooth closed manifold. This scale is built on the base of inner product distribution spaces of generalized smoothness given by an arbitrary positive function OR-varying at…
The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of generalized smoothness. The latter are the isotropic H\"ormander spaces $H^{s,\varphi}:=B_{2,\mu}$, with $\mu(\xi)=<\xi>^{s}\varphi(<\xi>)$ for…
We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product H\"ormander spaces for which an RO-varying radial function serves as a regularity index. These spaces do not depend on a…
We investigate general elliptic boundary-value problems in H\"ormander inner product spaces that form the extended Sobolev scale. The latter consists of all Hilbert spaces that are interpolation spaces with respect to the Sobolev Hilbert…
We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean domain with infinitely smooth boundary. We prove that the operator of the problem is bounded and Fredholm in appropriate pairs of H\"ormander…
The paper gives a survey of the modern results on elliptic problems on the H\"ormander function spaces. More precisely, elliptic problems are studied on a Hilbert scale of the isotropic H\"ormander spaces parametrized by a real number and a…
Parameter--elliptic pseudodifferential operators given on a closed smooth manifold are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev…
We investigate nonregular elliptic problems with boundary conditions of higher orders. We prove that these problems are Fredholm on appropriate pairs of inner product H\"ormander spaces that form a two-sided refined Sobolev scale. We also…
We investigate elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on…
We investigate Lawruk elliptic boundary-value problems for homogeneous differential equations in a two-sided refined Sobolev scale. These problems contain additional unknown functions in the boundary conditions of arbitrary orders. The…
We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an…
We study a system of pseudodifferential equations that is elliptic in the sense of Petrovskii on a closed compact smooth manifold. We prove that the operator generated by the system is Fredholm one on a refined two-sided scale of the…
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…
A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…
Parameter-elliptic boundary-value problems are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. The latter are the H\"ormander…
This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…
We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…
We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…
We give an application of interpolation with a function parameter to parabolic differential operators. We introduce the refined anisotropic Sobolev scale that consists of some Hilbert function spaces of generalized smoothness. The latter is…