Günter Hellwig (1926-2004) -- in memoriam
Hubert Kalf
TL;DR
This obituary chronicles Günter Hellwig's life and scientific impact, from wartime service to his rise as a leading PDE author and organizer. It highlights his early contributions, including the Lyapunov-type inequality $L_i \int_{a}^{b} \frac{|f''(x)|}{f(x)} dx > \frac{4}{b-a}$ for $f \in C^{0}([a,b]) \cap C^{2}((a,b))$, with $f>0$ in the interior and $f=0$ at the endpoints, and the elliptic-system index result ind(T) = 2 kappa + 1 tied to the boundary winding number kappa. It notes his foundational PDE textbooks (1960) and a Rellich-focused volume, his role in starting the Haack-Hellwig Oberwolfach Conferences (from 1961), and his influence as a mentor and community builder through Aachen's research culture and his public lectures on science and religion. It also emphasizes his lasting impact on spectral theory and operator theory, including Schrödinger operators, and concludes with a personal account of his death in 2004.
Abstract
Günter Hellwig was the author of influential textbooks on PDEs and differential operators of mathematical physics, an enthusiastic and inspiring teacher to generations of engineers, organiser of PDE conferences at Oberwolfach and a pioneer in index theory.