Elliptic problems in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity

TL;DR

This paper studies elliptic boundary value problems with unknown boundary distributions in low-regularity Besov and Triebel-Lizorkin spaces, demonstrating they induce Fredholm operators on suitable space pairs.

Contribution

It establishes the Fredholm property of elliptic problems with unknown boundary distributions in low-regularity Besov and Triebel-Lizorkin spaces, extending the theory to negative regularity orders.

Findings

Elliptic problems induce Fredholm bounded operators in these spaces.

The analysis covers spaces of arbitrary negative order.

Results extend elliptic theory to low-regularity function spaces.

Abstract

Elliptic problems with additional unknown distributions in boundary conditions are investigated in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity, specifically of an arbitrary negative order. We find that the problems induce Fredholm bounded operators on appropriate pairs of these spaces.