The Hardy constant: a review

Abstract

We present a review of results that have been obtained in the past twenty-five years concerning the $L^p$-Hardy inequality with distance to the boundary. We concentrate on results where the best Hardy constant is either computed exactly or estimated from below.

7 pages. To appear in the volume "Modern Problems in PDEs and Applications - Extended Abstracts of the 2023 Ghent Analysis and PDE Center Summer School", Research Perspectives Ghent Analysis and PDE Center, Trends in Mathematics, Springer. Editors: M. Chatzakou, J. Restrepo, M. Ruzhansky, B. Torebek, K. Van Bockstal