Introduction

Taming non-smoothness has been a major theme in the analysis of partial differential equations and other branches of analysis in the past decades. This monograph grew out of the PhD thesis of the author and presents their contribution to the field in a streamlined way. The content of this book is strongly based on the publications by the author together with his colleagues R. Brown, M. Egert, R. Haller, and P. Tolksdorf. Occasionally, the results in these articles are formulated in a more general manner. We tried to reduce technical difficulties as much as possible so that the reader gets an introduction to state-of-the-art results for square roots of elliptic systems in open sets with the least technical overhead possible.