Her dissertation, Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie, concerned isoperimetric inequalities and was jointly supervised by Joseph Hersch and Alfred Huber.
She was the first woman mathematician and one of the earliest women to earn a habilitation at ETH Zurich.
[4] She has studied destabilized elliptic equations with her friend and collaborator Maria Assunta Pozio.
It was only the second book to study the applications of isoperimetric inequalities in mathematical physics, after the 1951 book Isoperimetric Inequalities in Mathematical Physics by George Pólya and Gábor Szegő, and at the time of its publication was considerably more up-to-date on recent developments in the subject.
[6] In 2023, Bandle published the book Shape Optimization - Variations of Domains and Applications together with Alfred Wagner from RWTH Aachen University.