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.

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.