This volume collects six articles on selected topics at the frontier
between partial differential equations and spectral theory, written by
leading specialists in their respective field. The articles focus on
topics that are in the center of attention of current research, with
original contributions from the authors. They are written in a clear
expository style that makes them accessible to a broader audience. The
articles contain a detailed introduction and discuss recent progress,
provide additional motivation, and develop the necessary tools.
Moreover, the authors share their views on future developments,
hypotheses, and unsolved problems.