# Nonregular elliptic boundary-value problems and H\"ormander spaces

## TL;DR

This paper studies nonregular elliptic boundary-value problems with higher-order boundary conditions, establishing their Fredholm property and solution regularity within refined H"ormander spaces, advancing understanding of their analytical framework.

## Contribution

It introduces the use of H"ormander spaces in analyzing nonregular elliptic problems, proving Fredholmness and regularity results in a refined Sobolev scale.

## Key findings

- Problems are Fredholm on H"ormander spaces
- Generalized solutions exhibit regularity in these spaces
- Refined Sobolev scale effectively characterizes solution properties

## Abstract

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 prove a theorem on the regularity of generalized solutions to the problems in these spaces.