On some solvability theorems for pseudo-differential equations

TL;DR

This paper investigates solvability conditions for elliptic pseudo-differential equations and boundary value problems in Sobolev--Slobodetskii spaces with variable smoothness, providing criteria for unique solutions.

Contribution

It introduces new solvability theorems for elliptic pseudo-differential equations with boundary conditions in spaces with variable smoothness.

Findings

Sufficient conditions for unique solvability are established.

Analysis of boundary value problems in Sobolev--Slobodetskii spaces.

Application to half-space and cone geometries.

Abstract

We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient conditions for a unique solvability for such boundary value problems are described.