Elliptic operators and boundary problems in spaces of generalized smoothness

TL;DR

This paper surveys recent ten-year developments in elliptic boundary problems within H"ormander function spaces, highlighting foundational theory and applications in modern analysis.

Contribution

It consolidates and reviews advances in elliptic boundary problems in H"ormander spaces, emphasizing the authors' contributions and recent progress.

Findings

Comprehensive overview of elliptic boundary problems in H"ormander spaces

Systematic exposition of the theory and applications

Connection to modern analysis developments

Abstract

The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of this theory and some of its applications are systematically expounded in the monograph "H\"ormander Spaces, Interpolation, and Elliptic Problems" (De Gruyter, Berlin/Boston, 2014) by the first two authors of the survey.